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Jun Yin

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Published work

50 published item(s)

preprint2026arXiv

Power Reinforcement Post-Training of Text-to-Image Models with Super-Linear Advantage Shaping

Recently, post-training methods based on reinforcement learning, with a particular focus on Group Relative Policy Optimization (GRPO), have emerged as the robust paradigm for further advancement of text-to-image (T2I) models. However, these methods are often prone to reward hacking, wherein models exploit biases in imperfect reward functions rather than yielding genuine performance gains. In this work, we identify that normalization could lead to miscalibration and directly removing the prompt-level standard deviation term yields an optimal policy ascent direction that is linear in the advantage but still limits the separation of genuine signals from noise. To mitigate the above issues, we propose Super-Linear Advantage Shaping (SLAS) by revisiting the functional update from an information geometry perspective. By extending the Fisher-Rao information metric with advantage-dependent weighting, SLAS introduces a non-linear geometric structure that reshapes the local policy space. This design relaxes constraints along high-advantage directions to amplify informative updates, while tightening those in low-advantage regions to suppress illusory gradients. In addition, batch-level normalization is applied to stabilize training under varying reward scales. Extensive evaluations demonstrate that SLAS consistently surpasses the DanceGRPO baseline across multiple backbones and benchmarks. In particular, it yields faster training dynamics, improved out-of-domain performance on GenEval and UniGenBench++, and enhanced robustness to model scaling, while mitigating reward hacking and preserving semantic and compositional fidelity in generations.

preprint2024arXiv

Chirality tuning and reversing with resonant phase-change metasurfaces

Dynamic control of circular dichroism in photonic structures is critically important for compact spectrometers, stereoscopic displays, and information processing exploiting multiple degrees of freedom. Metasurfaces can help miniaturize chiral devices but only produce static and limited chiral responses. While external stimuli are able to tune resonances, their modulations are often weak, and reversing continuously the sign of circular dichroism is extremely challenging. Here, we demonstrate dynamically tunable chiral response of resonant metasurfaces supporting chiral bound states in the continuum combining them with phase-change materials. Phase transition between amorphous and crystalline phases allows to control chiral response and vary chirality rapidly from -0.947 to +0.958 backward and forward via chirality continuum. Our demonstrations underpin the rapid development of chiral photonics and its applications.

preprint2022arXiv

MASNet:Improve Performance of Siamese Networks with Mutual-attention for Remote Sensing Change Detection Tasks

Siamese networks are widely used for remote sensing change detection tasks. A vanilla siamese network has two identical feature extraction branches which share weights, these two branches work independently and the feature maps are not fused until about to be sent to a decoder head. However we find that it is critical to exchange information between two feature extraction branches at early stage for change detection task. In this work we present Mutual-Attention Siamese Network (MASNet), a general siamese network with mutual-attention plug-in, so to exchange information between the two feature extraction branches. We show that our modification improve the performance of siamese networks on multi change detection datasets, and it works for both convolutional neural network and visual transformer.

preprint2022arXiv

RPT++: Customized Feature Representation for Siamese Visual Tracking

While recent years have witnessed remarkable progress in the feature representation of visual tracking, the problem of feature misalignment between the classification and regression tasks is largely overlooked. The approaches of feature extraction make no difference for these two tasks in most of advanced trackers. We argue that the performance gain of visual tracking is limited since features extracted from the salient area provide more recognizable visual patterns for classification, while these around the boundaries contribute to accurately estimating the target state. We address this problem by proposing two customized feature extractors, named polar pooling and extreme pooling to capture task-specific visual patterns. Polar pooling plays the role of enriching information collected from the semantic keypoints for stronger classification, while extreme pooling facilitates explicit visual patterns of the object boundary for accurate target state estimation. We demonstrate the effectiveness of the task-specific feature representation by integrating it into the recent and advanced tracker RPT. Extensive experiments on several benchmarks show that our Customized Features based RPT (RPT++) achieves new state-of-the-art performances on OTB-100, VOT2018, VOT2019, GOT-10k, TrackingNet and LaSOT.

preprint2021arXiv

DCCRGAN: Deep Complex Convolution Recurrent Generator Adversarial Network for Speech Enhancement

Generative adversarial network (GAN) still exists some problems in dealing with speech enhancement (SE) task. Some GAN-based systems adopt the same structure from Pixel-to-Pixel directly without special optimization. The importance of the generator network has not been fully explored. Other related researches change the generator network but operate in the time-frequency domain, which ignores the phase mismatch problem. In order to solve these problems, a deep complex convolution recurrent GAN (DCCRGAN) structure is proposed in this paper. The complex module builds the correlation between magnitude and phase of the waveform and has been proved to be effective. The proposed structure is trained in an end-to-end way. Different LSTM layers are used in the generator network to sufficiently explore the speech enhancement performance of DCCRGAN. The experimental results confirm that the proposed DCCRGAN outperforms the state-of-the-art GAN-based SE systems.

preprint2021arXiv

Uniformly most reliable three-terminal graph of dense graphs

A graph $G$ with $k$ specified target vertices in vertex set is a $k$-terminal graph. The $k$-terminal reliability is the connection probability of the fixed $k$ target vertices in a $k$-terminal graph when every edge of this graph survives independently with probability $p$. For the class of two-terminal graphs with a large number of edges, Betrand, Goff, Graves and Sun constructed a locally most reliable two-terminal graph for $p$ close to $1$, and illustrated by a counterexample that this locally most reliable graph is not the uniformly most reliable two-terminal graph. At the same time, they also determined that there is a uniformly most reliable two-terminal graph in the class obtained by deleting an edge from the complete graph with two target vertices. This article focuses on the uniformly most reliable three-terminal graph of dense graphs with $n$ vertices and $m$ edges. First, we give the locally most reliable three-terminal graphs of $n$ and $m$ in certain ranges for $p$ close to $0$ and $1$. Then, it is proved that there is no uniformly most reliable three-terminal graph with specific $n$ and $m$, where $n\geq7$ and $\binom{n}{2}-\lfloor\frac{n-3}{2}\rfloor\leq m\leq\binom{n}{2}-2$. Finally, some uniformly most reliable graphs are given for $n$ vertices and $m$ edges, where $4\leq n\leq 6$ and $m=\binom{n}{2}-2$ or $n\geq5$ and $m=\binom{n}{2}-1$.

preprint2020arXiv

Convergence of eigenvector empirical spectral distribution of sample covariance matrices

The eigenvector empirical spectral distribution (VESD) is a useful tool in studying the limiting behavior of eigenvalues and eigenvectors of covariance matrices. In this paper, we study the convergence rate of the VESD of sample covariance matrices to the deformed Marčenko-Pastur (MP) distribution. Consider sample covariance matrices of the form $Σ^{1/2} X X^* Σ^{1/2}$, where $X=(x_{ij})$ is an $M\times N$ random matrix whose entries are independent random variables with mean zero and variance $N^{-1}$, and $Σ$ is a deterministic positive-definite matrix. We prove that the Kolmogorov distance between the expected VESD and the deformed MP distribution is bounded by $N^{-1+ε}$ for any fixed $ε>0$, provided that the entries $\sqrt{N}x_{ij}$ have uniformly bounded 6th moments and $|N/M-1|\ge τ$ for some constant $τ>0$. This result improves the previous one obtained in \cite{XYZ2013}, which gave the convergence rate $O(N^{-1/2})$ assuming $i.i.d.$ $X$ entries, bounded 10th moment, $Σ=I$ and $M<N$. Moreover, we also prove that under the finite $8$th moment assumption, the convergence rate of the VESD is $O(N^{-1/2+ε})$ almost surely for any fixed $ε>0$, which improves the previous bound $N^{-1/4+ε}$ in \cite{XYZ2013}.

preprint2020arXiv

Dynamics for droplet-based electricity generators

The finding of droplet-based electricity generator (DEG), based on the moving boundary of electrical double layer, has triggered great research enthusiasm, and a breakthrough in instantaneous electric power density was achieved recently. However, the dynamic mechanism for such droplet-based electricity generators remains elusive, impeding optimization of the DEG for practical applications. Through comprehensive experiments, we developed a dynamic model of surface charge density that can explain the underlying mechanism for the DEGs. The spreading droplet in touch with the top electrode can be equivalently regarded as an additional part of the top plate of the DEG capacitor, and the change of droplet area causes the change of surface charge density of the plates, driving electrons to migrate between the two plates. The insight of the dynamic mechanism paves a way for optimal design and practical applications of DEGs

preprint2020arXiv

Leveraging Multi-level Dependency of Relational Sequences for Social Spammer Detection

Much recent research has shed light on the development of the relation-dependent but content-independent framework for social spammer detection. This is largely because the relation among users is difficult to be altered when spammers attempt to conceal their malicious intents. Our study investigates the spammer detection problem in the context of multi-relation social networks, and makes an attempt to fully exploit the sequences of heterogeneous relations for enhancing the detection accuracy. Specifically, we present the Multi-level Dependency Model (MDM). The MDM is able to exploit user's long-term dependency hidden in their relational sequences along with short-term dependency. Moreover, MDM fully considers short-term relational sequences from the perspectives of individual-level and union-level, due to the fact that the type of short-term sequences is multi-folds. Experimental results on a real-world multi-relational social network demonstrate the effectiveness of our proposed MDM on multi-relational social spammer detection.

preprint2020arXiv

Random band matrices in the delocalized phase, III: Averaging fluctuations

We consider a general class of symmetric or Hermitian random band matrices $H=(h_{xy})_{x,y \in \llbracket 1,N\rrbracket^d}$ in any dimension $d\ge 1$, where the entries are independent, centered random variables with variances $s_{xy}=\mathbb E|h_{xy}|^2$. We assume that $s_{xy}$ vanishes if $|x-y|$ exceeds the band width $W$, and we are interested in the mesoscopic scale with $1\ll W\ll N$. Define the {\it{generalized resolvent}} of $H$ as $G(H,Z):=(H - Z)^{-1}$, where $Z$ is a deterministic diagonal matrix with entries $Z_{xx}\in \mathbb C_+$ for all $x$. Then we establish a precise high-probability bound on certain averages of polynomials of the resolvent entries. As an application of this fluctuation averaging result, we give a self-contained proof for the delocalization of random band matrices in dimensions $d\ge 2$. More precisely, for any fixed $d\ge 2$, we prove that the bulk eigenvectors of $H$ are delocalized in certain averaged sense if $N\le W^{1+\frac{d}{2}}$. This improves the corresponding results in \cite{HeMa2018} under the assumption $N\ll W^{1+\frac{d}{d+1}}$, and in \cite{ErdKno2013,ErdKno2011} under the assumption $N\ll W^{1+\frac{d}{6}}$. For 1D random band matrices, our fluctuation averaging result was used in \cite{PartII,PartI} to prove the delocalization conjecture and bulk universality for random band matrices with $N\ll W^{4/3}$.

preprint2020arXiv

RPT: Learning Point Set Representation for Siamese Visual Tracking

While remarkable progress has been made in robust visual tracking, accurate target state estimation still remains a highly challenging problem. In this paper, we argue that this issue is closely related to the prevalent bounding box representation, which provides only a coarse spatial extent of object. Thus an effcient visual tracking framework is proposed to accurately estimate the target state with a finer representation as a set of representative points. The point set is trained to indicate the semantically and geometrically significant positions of target region, enabling more fine-grained localization and modeling of object appearance. We further propose a multi-level aggregation strategy to obtain detailed structure information by fusing hierarchical convolution layers. Extensive experiments on several challenging benchmarks including OTB2015, VOT2018, VOT2019 and GOT-10k demonstrate that our method achieves new state-of-the-art performance while running at over 20 FPS.

preprint2019arXiv

Electronic phase separation in topological surface states of rhombohedral graphite

Of the two stable forms of graphite, hexagonal (HG) and rhombohedral (RG), the former is more common and has been studied extensively. RG is less stable, which so far precluded its detailed investigation, despite many theoretical predictions about the abundance of exotic interaction-induced physics. Advances in van der Waals heterostructure technology have now allowed us to make high-quality RG films up to 50 graphene layers thick and study their transport properties. We find that the bulk electronic states in such RG are gapped and, at low temperatures, electron transport is dominated by surface states. Because of topological protection, the surface states are robust and of high quality, allowing the observation of the quantum Hall effect, where RG exhibits phase transitions between gapless semimetallic phase and gapped quantum spin Hall phase with giant Berry curvature. An energy gap can also be opened in the surface states by breaking their inversion symmetry via applying a perpendicular electric field. Moreover, in RG films thinner than 4 nm, a gap is present even without an external electric field. This spontaneous gap opening shows pronounced hysteresis and other signatures characteristic of electronic phase separation, which we attribute to emergence of strongly-correlated electronic surface states.

preprint2018arXiv

Stellar population synthesis of galaxies with chemical evolution model

The derivation of accurate stellar populations of galaxies is a non-trivial task because of the well-known age-metallicity degeneracy. We aim to break this degeneracy by invoking a chemical evolution model(CEM) for isolated disk galaxy, where its metallicity enrichment history(MEH) is modelled to be tightly linked to its star formation history(SFH). Our CEM has been successfully tested on several local group dwarf galaxies whose SFHs and MEHs have been both independently measured from deep color-magnitude diagrams of individual stars. By introducing the CEM into the stellar population fitting algorithm as a prior, we expect that the SFH of galaxies could be better constrained.

preprint2016arXiv

Anisotropic local laws for random matrices

We develop a new method for deriving local laws for a large class of random matrices. It is applicable to many matrix models built from sums and products of deterministic or independent random matrices. In particular, it may be used to obtain local laws for matrix ensembles that are \emph{anisotropic} in the sense that their resolvents are well approximated by deterministic matrices that are not multiples of the identity. For definiteness, we present the method for sample covariance matrices of the form $Q := T X X^* T^*$, where $T$ is deterministic and $X$ is random with independent entries. We prove that with high probability the resolvent of $Q$ is close to a deterministic matrix, with an optimal error bound and down to optimal spectral scales. As an application, we prove the edge universality of $Q$ by establishing the Tracy-Widom-Airy statistics of the eigenvalues of $Q$ near the soft edges. This result applies in the single-cut and multi-cut cases. Further applications include the distribution of the eigenvectors and an analysis of the outliers and BBP-type phase transitions in finite-rank deformations; they will appear elsewhere. We also apply our method to Wigner matrices whose entries have arbitrary expectation, i.e. we consider $W+A$ where $W$ is a Wigner matrix and $A$ a Hermitian deterministic matrix. We prove the anisotropic local law for $W+A$ and use it to establish edge universality.

preprint2016arXiv

Neural Generative Question Answering

This paper presents an end-to-end neural network model, named Neural Generative Question Answering (GENQA), that can generate answers to simple factoid questions, based on the facts in a knowledge-base. More specifically, the model is built on the encoder-decoder framework for sequence-to-sequence learning, while equipped with the ability to enquire the knowledge-base, and is trained on a corpus of question-answer pairs, with their associated triples in the knowledge-base. Empirical study shows the proposed model can effectively deal with the variations of questions and answers, and generate right and natural answers by referring to the facts in the knowledge-base. The experiment on question answering demonstrates that the proposed model can outperform an embedding-based QA model as well as a neural dialogue model trained on the same data.

preprint2016arXiv

Polaron Self-localization in White-light Emitting Hybrid Perovskites

Two-dimensional (2D) perovskites with general formula $APbX_4$ are attracting increasing interest as solution processable, white-light emissive materials. Recent studies have shown that their broadband emission is related to the formation of intra-gap color centers; however, the nature and dynamics of the emissive species have remained elusive. Here we show that the broadband photoluminescence of the 2D perovskites $(EDBE)PbCl_4$ and $(EDBE)PbBr_4$ stems from the localization of small polarons within the lattice distortion field. Using a combination of spectroscopic techniques and first-principles calculations, we infer the formation of ${Pb_2}^{3+}$, $Pb^{3+}$, and ${X_2}^-$ (where X=Cl or Br) species confined within the inorganic perovskite framework. Due to strong Coulombic interactions, these species retain their original excitonic character and form self-trapped polaron-excitons acting as radiative color centers. These findings are expected to be applicable to a broad class of white-light emitting perovskites with large polaron relaxation energy.

preprint2016arXiv

Universality for a class of random band matrices

We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, $W\sim N$. All previous results concerning universality of non-Gaussian random matrices are for mean-field models. By relying on a new mean-field reduction technique, we deduce universality from quantum unique ergodicity for band matrices.

preprint2015arXiv

An Apparent Redshift Dependence of Quasar Continuum: Implication for Cosmic Dust Extinction?

We investigate the luminosity and redshift dependence of the quasar continuum by means of composite spectrum using a large non-BAL radio-quiet quasar sample drawn from the Sloan Digital Sky Survey. Quasar continuum slopes in the UV-Opt band are measured at two different wavelength ranges, i.e., $α_{\nu12}$ ($1000\sim 2000 \rmÅ$) and $α_{\nu24}$ ($2000 \sim 4000 \rmÅ$) derived from power law fitting. Generally, the UV spectra slope becomes harder (higher $α_ν$) towards higher bolometric luminosity. On the other hand, when quasars are further grouped into luminosity bins, we find both $α_{\nu12}$ and $α_{\nu24}$ show significant anti-correlation with redshift (i.e., quasar continuum becomes redder towards higher redshift). We suggest that the cosmic dust extinction is very likely the cause of this observed $α_ν-z$ relation. We build a simple cosmic dust extinction model to quantify the observed reddening tendency and find an effective dust density $nσ_v \sim 10^{-5}h~\rm Mpc^{-1}$ at $z<1.5$. The other possibilities that could produce such a reddening effect have also been discussed.

preprint2015arXiv

Beam transport experiment with a new kicker control system on the HIRFL-CSR

The kicker control system was used for beam extraction and injection between two cooling storage rings (CSRs) at the Heavy Ion Research Facility in Lanzhou (HIRFL). To meet the requirements of special physics experiments, the kicker controller was upgraded. The new controller was designed based on ARM+DSP+FPGA technology and monolithic circuit architecture, which can achieve a precision time delay of 2.5 ns. In September 2014, the new kicker control system was installed in the kicker field, and the test experiment using the system was completed. In addition, a pre-trigger signal was provided by the controller, which was designed to synchronize the beam diagnostic system and physics experiments. Experimental results indicate that the phenomena of "missed kick" and "inefficient kick" were not observed, and the multichannel trigger signals' delay could be adjusted individually for kick power supplies in digitization; thus, the beam transport efficiency was improved compared with that of the original system. The fast extraction and injection experiment was successfully completed based on the new kicker control systems for HIRFL-CSR.

preprint2015arXiv

Fixed energy universality for generalized Wigner matrices

We prove the Wigner-Dyson-Mehta conjecture at fixed energy in the bulk of the spectrum for generalized symmetric and Hermitian Wigner matrices. Previous results concerning the universality of random matrices either require an averaging in the energy parameter or they hold only for Hermitian matrices if the energy parameter is fixed. We develop a homogenization theory of the Dyson Brownian motion and show that microscopic universality follows from mesoscopic statistics.

preprint2015arXiv

Isotropic Local Laws for Sample Covariance and Generalized Wigner Matrices

We consider sample covariance matrices of the form $X^*X$, where $X$ is an $M \times N$ matrix with independent random entries. We prove the isotropic local Marchenko-Pastur law, i.e. we prove that the resolvent $(X^* X - z)^{-1}$ converges to a multiple of the identity in the sense of quadratic forms. More precisely, we establish sharp high-probability bounds on the quantity $\langle v, (X^* X - z)^{-1} w \rangle - \langle v,w\rangle m(z)$, where $m$ is the Stieltjes transform of the Marchenko-Pastur law and $v, w \in \mathbb C^N$. We require the logarithms of the dimensions $M$ and $N$ to be comparable. Our result holds down to scales $Im z \geq N^{-1+ε}$ and throughout the entire spectrum away from 0. We also prove analogous results for generalized Wigner matrices.

preprint2015arXiv

On the principal components of sample covariance matrices

We introduce a class of $M \times M$ sample covariance matrices $\mathcal Q$ which subsumes and generalizes several previous models. The associated population covariance matrix $Σ= \mathbb E \cal Q$ is assumed to differ from the identity by a matrix of bounded rank. All quantities except the rank of $Σ- I_M$ may depend on $M$ in an arbitrary fashion. We investigate the principal components, i.e.\ the top eigenvalues and eigenvectors, of $\mathcal Q$. We derive precise large deviation estimates on the generalized components $\langle \mathbf w, \boldsymbol ξ_i \rangle$ of the outlier and non-outlier eigenvectors $\boldsymbol ξ_i$. Our results also hold near the so-called BBP transition, where outliers are created or annihilated, and for degenerate or near-degenerate outliers. We believe the obtained rates of convergence to be optimal. In addition, we derive the asymptotic distribution of the generalized components of the non-outlier eigenvectors. A novel observation arising from our results is that, unlike the eigenvalues, the eigenvectors of the principal components contain information about the \emph{subcritical} spikes of $Σ$. The proofs use several results on the eigenvalues and eigenvectors of the uncorrelated matrix $\mathcal Q$, satisfying $\mathbb E \mathcal Q = I_M$, as input: the isotropic local Marchenko-Pastur law established in [9], level repulsion, and quantum unique ergodicity of the eigenvectors. The latter is a special case of a new universality result for the joint eigenvalue-eigenvector distribution.

preprint2015arXiv

The Dynamic Range of LZ

The electronics of the LZ experiment, the 7-tonne dark matter detector to be installed at the Sanford Underground Research Facility (SURF), is designed to permit studies of physics where the energies deposited range from 1 keV of nuclear-recoil energy up to 3,000 keV of electron-recoil energy. The system is designed to provide a 70% efficiency for events that produce three photoelectrons in the photomultiplier tubes (PMTs). This corresponds approximately to the lowest energy threshold achievable in multi-tonne time-projection chambers, and drives the noise specifications for the front end. The upper limit of the LZ dynamic range is defined to accommodate the electroluminescence (S2) signals. The low-energy channels of the LZ amplifiers provide the dynamic range required for the tritium and krypton calibrations. The high-energy channels provide the dynamic range required to measure the activated Xe lines.

preprint2015arXiv

The K giant stars from the LAMOST survey data II: the Hercules stream in radial migration

We estimate the age for the individual stars located at the lower part of the red giant branch from the LAMOST DR2 K giant sample. Taking into account the selection effects and the volume completeness, the age--metallicity map for the stars located between 0.3 and 1.5 kpc from the Sun is obtained. A significant substructure (denoted as the \it{narrow stripe}) located from (age, [Fe/H])$\sim$(5, 0.4) to (10 Gyr, -0.4 dex) in the age--metallicity map is clearly identified. Moreover, the \it{narrow stripe} stars are found the dominate contributors to several velocity substructures, including the well-known Hercules stream. The substantially large difference between the observed guiding-center radii and the birth radii inferred from the age--metallicity relation is evident that the \it{narrow stripe} stars have been radially migrated from about R$\sim4$ kpc to the solar neighborhood. This implies that the Hercules stream may not be owe to the resonance associated with the bar, but may be the kinematic imprint of the inner disk and later moved out due to radial migration. We estimate that the traveling speed of the radial migration are roughly 1.1$\pm0.1$ kpc Gyr$^{-1}$, equivalent with about $1.1\pm0.1$ km s$^{-1}$. This is in agreement with the median $v_R$ of $2.6^{+1.8}_{-1.9}$ km s$^{-1}$ of the \it{narrow stripe}. We also obtain that about one third stars in the solar neighborhood are radially migrated from around 4 kpc. Finally, we find that the radial migration does not lead to additional disk thickening according to the distribution of $z_{max}$.

preprint2015arXiv

The Most Massive Ultra-Compact Dwarf Galaxy in the Virgo Cluster

We report on the properties of the most massive ultra-compact dwarf galaxy (UCD) in the nearby Virgo Cluster of galaxies using imaging from the Next Generation Virgo Cluster Survey (NGVS) and spectroscopy from Keck/DEIMOS. This object (M59-UCD3) appears to be associated with the massive Virgo galaxy M59 (NGC 4621), has an integrated velocity dispersion of 78 km/s, a dynamical mass of $3.7\times10^8 M_\odot$, and an effective radius ($R_e$) of 25 pc. With an effective surface mass density of $9.4\times10^{10} M_\odot/kpc^2$, it is the densest galaxy in the local Universe discovered to date, surpassing the density of the luminous Virgo UCD, M60-UCD1. M59-UCD3 has a total luminosity of $M_{g'}=-14.2$ mag, and a spectral energy distribution consistent with an old (14 Gyr) stellar population with [Fe/H]=0.0 and [$α$/Fe]=+0.2. We also examine deep imaging around M59 and find a broad low surface brightness stream pointing towards M59-UCD3, which may represent a tidal remnant of the UCD progenitor. This UCD, along with similar objects like M60-UCD1 and M59cO, likely represents an extreme population of tidally stripped galaxies more akin to larger and more massive compact early-type galaxies than to nuclear star clusters in present-day dwarf galaxies.

preprint2014arXiv

The outliers of a deformed Wigner matrix

We derive the joint asymptotic distribution of the outlier eigenvalues of an additively deformed Wigner matrix $H$. Our only assumptions on the deformation are that its rank be fixed and its norm bounded. Our results extend those of [The isotropic semicircle law and deformation of Wigner matrices. Preprint] by admitting overlapping outliers and by computing the joint distribution of all outliers. In particular, we give a complete description of the failure of universality first observed in [Ann. Probab. 37 (2009) 1-47; Ann. Inst. Henri Poincaré Probab. Stat. 48 (1013) 107-133; Free convolution with a semi-circular distribution and eigenvalues of spiked deformations of Wigner matrices. Preprint]. We also show that, under suitable conditions, outliers may be strongly correlated even if they are far from each other. Our proof relies on the isotropic local semicircle law established in [The isotropic semicircle law and deformation of Wigner matrices. Preprint]. The main technical achievement of the current paper is the joint asymptotics of an arbitrary finite family of random variables of the form $\langle\mathbf{v},(H-z)^{-1}\mathbf{w}\rangle$.

preprint2014arXiv

Universality of covariance matrices

In this paper we prove the universality of covariance matrices of the form $H_{N\times N}={X}^{\dagger}X$ where $X$ is an ${M\times N}$ rectangular matrix with independent real valued entries $x_{ij}$ satisfying $\mathbb{E}x_{ij}=0$ and $\mathbb{E}x^2_{ij}={\frac{1}{M}}$, $N$, $M\to \infty$. Furthermore it is assumed that these entries have sub-exponential tails or sufficiently high number of moments. We will study the asymptotics in the regime $N/M=d_N\in(0,\infty),\lim_{N\to\infty}d_N\neq0,\infty$. Our main result is the edge universality of the sample covariance matrix at both edges of the spectrum. In the case $\lim_{N\to\infty}d_N=1$, we only focus on the largest eigenvalue. Our proof is based on a novel version of the Green function comparison theorem for data matrices with dependent entries. En route to proving edge universality, we establish that the Stieltjes transform of the empirical eigenvalue distribution of $H$ is given by the Marcenko-Pastur law uniformly up to the edges of the spectrum with an error of order $(Nη)^{-1}$ where $η$ is the imaginary part of the spectral parameter in the Stieltjes transform. Combining these results with existing techniques we also show bulk universality of covariance matrices. All our results hold for both real and complex valued entries.

preprint2013arXiv

Delocalization and Diffusion Profile for Random Band Matrices

We consider Hermitian and symmetric random band matrices $H = (h_{xy})$ in $d \geq 1$ dimensions. The matrix entries $h_{xy}$, indexed by $x,y \in (\bZ/L\bZ)^d$, are independent, centred random variables with variances $s_{xy} = \E |h_{xy}|^2$. We assume that $s_{xy}$ is negligible if $|x-y|$ exceeds the band width $W$. In one dimension we prove that the eigenvectors of $H$ are delocalized if $W\gg L^{4/5}$. We also show that the magnitude of the matrix entries $\abs{G_{xy}}^2$ of the resolvent $G=G(z)=(H-z)^{-1}$ is self-averaging and we compute $\E \abs{G_{xy}}^2$. We show that, as $L\to\infty$ and $W\gg L^{4/5}$, the behaviour of $\E |G_{xy}|^2$ is governed by a diffusion operator whose diffusion constant we compute. Similar results are obtained in higher dimensions.

preprint2013arXiv

Local Circular Law for Random Matrices

The circular law asserts that the spectral measure of eigenvalues of rescaled random matrices without symmetry assumption converges to the uniform measure on the unit disk. We prove a local version of this law at any point $z$ away from the unit circle. More precisely, if $ | |z| - 1 | \ge τ$ for arbitrarily small $τ> 0$, the circular law is valid around $z$ up to scale $N^{-1/2+ \e}$ for any $\e > 0$ under the assumption that the distributions of the matrix entries satisfy a uniform subexponential decay condition.

preprint2013arXiv

Spectral statistics of Erdős-Rényi graphs I: Local semicircle law

We consider the ensemble of adjacency matrices of Erdős-Rényi random graphs, that is, graphs on $N$ vertices where every edge is chosen independently and with probability $p\equiv p(N)$. We rescale the matrix so that its bulk eigenvalues are of order one. We prove that, as long as $pN\to\infty$ (with a speed at least logarithmic in $N$), the density of eigenvalues of the Erdős-Rényi ensemble is given by the Wigner semicircle law for spectral windows of length larger than $N^{-1}$ (up to logarithmic corrections). As a consequence, all eigenvectors are proved to be completely delocalized in the sense that the $\ell^{\infty}$-norms of the $\ell^2$-normalized eigenvectors are at most of order $N^{-1/2}$ with a very high probability. The estimates in this paper will be used in the companion paper [Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues (2011) Preprint] to prove the universality of eigenvalue distributions both in the bulk and at the spectral edges under the further restriction that $pN\gg N^{2/3}$.

preprint2013arXiv

The local circular law II: the edge case

In the first part of this article, we proved a local version of the circular law up to the finest scale $N^{-1/2+ \e}$ for non-Hermitian random matrices at any point $z \in \C$ with $||z| - 1| > c $ for any $c>0$ independent of the size of the matrix. Under the main assumption that the first three moments of the matrix elements match those of a standard Gaussian random variable after proper rescaling, we extend this result to include the edge case $ |z|-1=\oo(1)$. Without the vanishing third moment assumption, we prove that the circular law is valid near the spectral edge $ |z|-1=\oo(1)$ up to scale $N^{-1/4+ \e}$.

preprint2013arXiv

The Local Circular Law III: General Case

In the first part of this article series, Bourgade, Yau and the author of this paper proved a local version of the circular law up to the finest scale $N^{-1/2+ \e}$ for non-Hermitian random matrices at any point $z \in \C$ with $||z| - 1| > c $ for any $c>0$ independent of the size of the matrix. In the second part, they extended this result to include the edge case $ |z|-1=\oo(1)$, under the main assumption that the third moments of the matrix elements vanish. (Without the vanishing third moment assumption, they proved that the circular law is valid near the spectral edge $ |z|-1=\oo(1)$ up to scale $N^{-1/4+ \e}$.) In this paper, we will remove this assumption, i.e. we prove a local version of the circular law up to the finest scale $N^{-1/2+ \e}$ for non-Hermitian random matrices at any point $z \in \C$.

preprint2013arXiv

The Local Semicircle Law for a General Class of Random Matrices

We consider a general class of $N\times N$ random matrices whose entries $h_{ij}$ are independent up to a symmetry constraint, but not necessarily identically distributed. Our main result is a local semicircle law which improves previous results [14] both in the bulk and at the edge. The error bounds are given in terms of the basic small parameter of the model, $\max_{i,j} \E \abs{h_{ij}}^2$. As a consequence, we prove the universality of the local $n$-point correlation functions in the bulk spectrum for a class of matrices whose entries do not have comparable variances, including random band matrices with band width $W\gg N^{1-\e_n}$ with some $\e_n>0$ and with a negligible mean-field component. In addition, we provide a coherent and pedagogical proof of the local semicircle law, streamlining and strengthening previous arguments from [3,4,16].

preprint2012arXiv

A Necessary and Sufficient Condition for Edge Universality of Wigner matrices

In this paper, we prove a necessary and sufficient condition for Tracy-Widom law of Wigner matrices. Consider $N \times N$ symmetric Wigner matrices $H$ with $H_{ij} = N^{-1/2} x_{ij}$, whose upper right entries $x_{ij}$ $(1\le i< j\le N)$ are $i.i.d.$ random variables with distribution $μ$ and diagonal entries $x_{ii}$ $(1\le i\le N)$ are $i.i.d.$ random variables with distribution $\wt μ$. The means of $μ$ and $\wt μ$ are zero, the variance of $μ$ is 1, and the variance of $\wt μ$ is finite. We prove that Tracy-Widom law holds if and only if $\lim_{s\to \infty}s^4\p(|x_{12}| \ge s)=0$. The same criterion holds for Hermitian Wigner matrices.

preprint2012arXiv

Edge universality of correlation matrices

Let $\widetilde{X}_{M\times N}$ be a rectangular data matrix with independent real-valued entries $[\widetilde{x}_{ij}]$ satisfying $\mathbb {E}\widetilde{x}_{ij}=0$ and $\mathbb {E}\widetilde{x}^2_{ij}=\frac{1}{M}$, $N,M\to\infty$. These entries have a subexponential decay at the tails. We will be working in the regime $N/M=d_N,\lim_{N\to\infty}d_N\neq0,1,\infty$. In this paper we prove the edge universality of correlation matrices ${X}^{\dagger}X$, where the rectangular matrix $X$ (called the standardized matrix) is obtained by normalizing each column of the data matrix $\widetilde{X}$ by its Euclidean norm. Our main result states that asymptotically the $k$-point ($k\geq1$) correlation functions of the extreme eigenvalues (at both edges of the spectrum) of the correlation matrix ${X}^{\dagger}X$ converge to those of the Gaussian correlation matrix, that is, Tracy-Widom law, and, thus, in particular, the largest and the smallest eigenvalues of ${X}^{\dagger}X$ after appropriate centering and rescaling converge to the Tracy-Widom distribution. The asymptotic distribution of extreme eigenvalues of the Gaussian correlation matrix has been worked out only recently. As a corollary of the main result in this paper, we also obtain that the extreme eigenvalues of Gaussian correlation matrices are asymptotically distributed according to the Tracy-Widom law. The proof is based on the comparison of Green functions, but the key obstacle to be surmounted is the strong dependence of the entries of the correlation matrix. We achieve this via a novel argument which involves comparing the moments of product of the entries of the standardized data matrix to those of the raw data matrix. Our proof strategy may be extended for proving the edge universality of other random matrix ensembles with dependent entries and hence is of independent interest.

preprint2012arXiv

Exceptional high Seebeck Coefficient and Gas-Flow-Induced Voltage in Multilayer Graphene

Monolayer graphene shows Seebeck coefficient several times and gas-flow-induced voltage twenty times higher than that of bulk graphite. Here we find that the Seebeck coefficient of multilayer graphene increases monotonically with increasing layer and reaches its peak value at hexa-layer ~77% higher than for monolayer and then decreases, although the electric resistance decreases monotonically with increasing layer. The flow-induced voltage is significantly higher in 2, 4, 5, 6, 7 layered graphene than in 1, 3, 8 layered one, against the prevailing view that it should be proportional to Seebeck coefficient. These thickness effects are also in sharp contrast to that in continuous aluminum nanofilms.

preprint2012arXiv

Spectral Statistics of Erd{\H o}s-Rényi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues

We consider the ensemble of adjacency matrices of Erd{\H o}s-Rényi random graphs, i.e.\ graphs on $N$ vertices where every edge is chosen independently and with probability $p \equiv p(N)$. We rescale the matrix so that its bulk eigenvalues are of order one. Under the assumption $p N \gg N^{2/3}$, we prove the universality of eigenvalue distributions both in the bulk and at the edge of the spectrum. More precisely, we prove (1) that the eigenvalue spacing of the Erd{\H o}s-Rényi graph in the bulk of the spectrum has the same distribution as that of the Gaussian orthogonal ensemble; and (2) that the second largest eigenvalue of the Erd{\H o}s-Rényi graph has the same distribution as the largest eigenvalue of the Gaussian orthogonal ensemble. As an application of our method, we prove the bulk universality of generalized Wigner matrices under the assumption that the matrix entries have at least $4 + ε$ moments.

preprint2012arXiv

The Evolution and Star Formation History of M33

We construct a parameterized model to explore the main properties of the star formation history of M33. We assume that the disk originates and grows by the primordial gas infall and adopt the simple form of gas accretion rate with one free parameter, the infall time-scale. We also include the contribution of gas outflow process. A major update of the model is that we adopt a molecular hydrogen correlated star formation law and calculate the evolution of the atomic and molecular gas separately. Comparisons between the model predictions and the observational data show that the model predictions are very sensitive to the adopted infall time-scale, while the gas outflow process mainly influences the metallicity profile. The model adopting a moderate outflow rate and an inside-out formation scenario can be in good agreement with most of observed constraints of M33 disk. We also compare the model predictions based on the molecular hydrogen correlated star formation law and that based on the Kennicutt star formation law. Our results imply that the molecular hydrogen correlated star formation law should be preferred to describe the evolution of the M33 disk, especially the radial distributions of both the cold gas and the stellar population.

preprint2012arXiv

The Isotropic Semicircle Law and Deformation of Wigner Matrices

We analyse the spectrum of additive finite-rank deformations of $N \times N$ Wigner matrices $H$. The spectrum of the deformed matrix undergoes a transition, associated with the creation or annihilation of an outlier, when an eigenvalue $d_i$ of the deformation crosses a critical value $\pm 1$. This transition happens on the scale $|d_i| - 1 \sim N^{-1/3}$. We allow the eigenvalues $d_i$ of the deformation to depend on $N$ under the condition $|\abs{d_i} - 1| \geq (\log N)^{C \log \log N} N^{-1/3}$. We make no assumptions on the eigenvectors of the deformation. In the limit $N \to \infty$, we identify the law of the outliers and prove that the non-outliers close to the spectral edge have a universal distribution coinciding with that of the extremal eigenvalues of a Gaussian matrix ensemble. A key ingredient in our proof is the \emph{isotropic local semicircle law}, which establishes optimal high-probability bounds on the quantity $< v,[(H - z)^{-1} - m(z) 1] w >$, where $m(z)$ is the Stieltjes transform of Wigner's semicircle law and $v, w$ are arbitrary deterministic vectors.

preprint2011arXiv

Bulk universality for generalized Wigner matrices

Consider $N\times N$ Hermitian or symmetric random matrices $H$ where the distribution of the $(i,j)$ matrix element is given by a probability measure $ν_{ij}$ with a subexponential decay. Let $σ_{ij}^2$ be the variance for the probability measure $ν_{ij}$ with the normalization property that $\sum_{i} σ^2_{ij} = 1$ for all $j$. Under essentially the only condition that $c\le N σ_{ij}^2 \le c^{-1}$ for some constant $c>0$, we prove that, in the limit $N \to \infty$, the eigenvalue spacing statistics of $H$ in the bulk of the spectrum coincide with those of the Gaussian unitary or orthogonal ensemble (GUE or GOE). We also show that for band matrices with bandwidth $M$ the local semicircle law holds to the energy scale $M^{-1}$.

preprint2011arXiv

Chemical Evolution of Dwarf Irregular and Blue Compact Galaxies

Dwarf irregular and blue compact galaxies are very interesting objects since they are relatively simple and unevolved. We present new models for the chemical evolution of these galaxies by assuming different regimes of star formation (bursting and continuous) and different kinds of galactic winds (normal and metal-enhanced). Our results show that in order to reproduce all the properties of these galaxies, including the spread in the chemical abundances, the star formation should have proceeded in bursts and the number of bursts should be not larger than 10 in each galaxy, and that metal-enhanced galactic winds are required. A metal-enhanced wind efficiency increasing with galactic mass can by itself reproduce the observed mass-metallicity relation although also an increasing efficiency of star formation and/or number and/or duration of bursts can equally well reproduce such a relation. Metal enhanced winds together with an increasing amount of star formation with galactic mass are required to explain most of the properties of these galaxies. Normal galactic winds, where all the gas is lost at the same rate, do not reproduce the features of these galaxies. We suggest that these galaxies should have suffered a different number of bursts varying from 2 to 10 and that the efficiency of metal-enhanced winds should have been not too high ($λ_{mw}\sim1$). We predict for these galaxies present time Type Ia SN rates from 0.00084 and 0.0023 per century. Finally, by comparing the abundance patterns of Damped Lyman-$α$ objects with our models we conclude that they are very likely the progenitors of the present day dwarf irregulars. (abridged)

preprint2011arXiv

Eigenvector Distribution of Wigner Matrices

We consider $N\times N$ Hermitian or symmetric random matrices with independent entries. The distribution of the $(i,j)$-th matrix element is given by a probability measure $ν_{ij}$ whose first two moments coincide with those of the corresponding Gaussian ensemble. We prove that the joint probability distribution of the components of eigenvectors associated with eigenvalues close to the spectral edge agrees with that of the corresponding Gaussian ensemble. For eigenvectors associated with bulk eigenvalues, the same conclusion holds provided the first four moments of the distribution $ν_{ij}$ coincide with those of the corresponding Gaussian ensemble. More generally, we prove that the joint eigenvector-eigenvalue distributions near the spectral edge of two generalized Wigner ensembles agree, provided that the first two moments of the entries match and that one of the ensembles satisfies a level repulsion estimate. If in addition the first four moments match then this result holds also in the bulk.

preprint2011arXiv

Enhanced Gas-Flow-Induced Voltage in Graphene

We show by systemically experimental investigation that gas-flow-induced voltage in monolayer graphene is more than twenty times of that in bulk graphite. Examination over samples with sheet resistances ranging from 307 to 1600 Ω/sq shows that the induced voltage increase with the resistance and can be further improved by controlling the quality and doping level of graphene. The induced voltage is nearly independent of the substrate materials and can be well explained by the interplay of Bernoulli's principle and the carrier density dependent Seebeck coefficient. The results demonstrate that graphene has great potential for flow sensors and energy conversion devices.

preprint2011arXiv

Rigidity of Eigenvalues of Generalized Wigner Matrices

Consider $N\times N$ hermitian or symmetric random matrices $H$ with independent entries, where the distribution of the $(i,j)$ matrix element is given by the probability measure $ν_{ij}$ with zero expectation and with variance $σ_{ij}^2$. We assume that the variances satisfy the normalization condition $\sum_{i} σ^2_{ij} = 1$ for all $j$ and that there is a positive constant $c$ such that $c\le N σ_{ij}^2 \le c^{-1}$. We further assume that the probability distributions $ν_{ij}$ have a uniform subexponential decay. We prove that the Stieltjes transform of the empirical eigenvalue distribution of $H$ is given by the Wigner semicircle law uniformly up to the edges of the spectrum with an error of order $ (N η)^{-1}$ where $η$ is the imaginary part of the spectral parameter in the Stieltjes transform. There are three corollaries to this strong local semicircle law: (1) Rigidity of eigenvalues: If $γ_j =γ_{j,N}$ denotes the {\it classical location} of the $j$-th eigenvalue under the semicircle law ordered in increasing order, then the $j$-th eigenvalue $λ_j$ is close to $γ_j$ in the sense that for any $ξ>1$ there is a constant $L$ such that \[\mathbb P \Big (\exists \, j : \; |λ_j-γ_j| \ge (\log N)^L \Big [ \min \big (\, j, N-j+1 \, \big) \Big ]^{-1/3} N^{-2/3} \Big) \le C\exp{\big[-c(\log N)^ξ \big]} \] for $N$ large enough. (2) The proof of the {\it Dyson's conjecture} \cite{Dy} which states that the time scale of the Dyson Brownian motion to reach local equilibrium is of order $N^{-1}$. (3) The edge universality holds in the sense that the probability distributions of the largest (and the smallest) eigenvalues of two generalized Wigner ensembles are the same in the large $N$ limit provided that the second moments of the two ensembles are identical.

preprint2011arXiv

Universality for generalized Wigner matrices with Bernoulli distribution

The universality for the eigenvalue spacing statistics of generalized Wigner matrices was established in our previous work \cite{EYY} under certain conditions on the probability distributions of the matrix elements. A major class of probability measures excluded in \cite{EYY} are the Bernoulli measures. In this paper, we extend the universality result of \cite{EYY} to include the Bernoulli measures so that the only restrictions on the probability distributions of the matrix elements are the subexponential decay and the normalization condition that the variances in each row sum up to one. The new ingredient is a strong local semicircle law which improves the error estimate on the Stieltjes transform of the empirical measure of the eigenvalues from the order $(N η)^{-1/2}$ to $(N η)^{-1}$. Here $η$ is the imaginary part of the spectral parameter in the definition of the Stieltjes transform and $N$ is the size of the matrix.

preprint2010arXiv

A Lower Bound on the Ground State Energy of Dilute Bose Gas

Consider an N-Boson system interacting via a two-body repulsive short-range potential $V$ in a three dimensional box $Λ$ of side length $L$. We take the limit $N, L \to \infty$ while keeping the density $ρ= N / L^3$ fixed and small. We prove a new lower bound for its ground state energy per particle $$\frac{E(N, Λ)}{N} \geq 4 πa ρ[ 1 - O(ρ^{1/3} |\log ρ|^3) ],$$ as $ρ\to 0$, where $a$ is the scattering length of $V$.

preprint2010arXiv

Free Energies of Dilute Bose gases: upper bound

We derive a upper bound on the free energy of a Bose gas system at density $ρ$ and temperature $T$. In combination with the lower bound derived previously by Seiringer \cite{RS1}, our result proves that in the low density limit, i.e., when $a^3ρ\ll 1$, where $a$ denotes the scattering length of the pair-interaction potential, the leading term of $Δf$ the free energy difference per volume between interacting and ideal Bose gases is equal to $4πa (2ρ^2-[ρ-\rhoc]^2_+)$. Here, $\rhoc(T)$ denotes the critical density for Bose-Einstein condensation (for the ideal gas), and $[\cdot ]_+$ $=$ $\max\{\cdot, 0\}$ denotes the positive part.

preprint2010arXiv

The chemical evolution of IC10

Dwarf irregular galaxies are relatively simple unevolved objects where it is easy to test models of galactic chemical evolution. We attempt to determine the star formation and gas accretion history of IC10, a local dwarf irregular for which abundance, gas, and mass determinations are available. We apply detailed chemical evolution models to predict the evolution of several chemical elements (He, O, N, S) and compared our predictions with the observational data. We consider additional constraints such as the present-time gas fraction, the star formation rate (SFR), and the total estimated mass of IC10. We assume a dark matter halo for this galaxy and study the development of a galactic wind. We consider different star formation regimes: bursting and continuous. We explore different wind situations: i) normal wind, where all the gas is lost at the same rate and ii) metal-enhanced wind, where metals produced by supernovae are preferentially lost. We study a case without wind. We vary the star formation efficiency (SFE), the wind efficiency, and the time scale of the gas infall, which are the most important parameters in our models. We find that only models with metal-enhanced galactic winds can reproduce the properties of IC10. The star formation must have proceeded in bursts rather than continuously and the bursts must have been less numerous than ~10 over the whole galactic lifetime. Finally, IC10 must have formed by a slow process of gas accretion with a timescale of the order of 8 Gyr.

preprint2010arXiv

The local relaxation flow approach to universality of the local statistics for random matrices

We present a generalization of the method of the local relaxation flow to establish the universality of local spectral statistics of a broad class of large random matrices. We show that the local distribution of the eigenvalues coincides with the local statistics of the corresponding Gaussian ensemble provided the distribution of the individual matrix element is smooth and the eigenvalues ${x_j}_{j=1}^N$ are close to their classical location ${γ_j}_{j=1}^N$ determined by the limiting density of eigenvalues. Under the scaling where the typical distance between neighboring eigenvalues is of order 1/N, the necessary apriori estimate on the location of eigenvalues requires only to know that $\E |x_j - γ_j |^2 \le N^{-1-\e}$ on average. This information can be obtained by well established methods for various matrix ensembles. We demonstrate the method by proving local spectral universality for Wishart matrices.

preprint2008arXiv

The Ground State Energy of Dilute Bose Gas in Potentials with Positive Scattering Length

The leading term of the ground state energy/particle of a dilute gas of bosons with mass $m$ in the thermodynamic limit is $2π\hbar^2 a ρ/m$ when the density of the gas is $ρ$, the interaction potential is non-negative and the scattering length $a$ is positive. In this paper, we generalize the upper bound part of this result to any interaction potential with positive scattering length, i.e, $a>0$ and the lower bound part to some interaction potentials with shallow and/or narrow negative parts.