A note on pair dependent linear statistics with slowly growing variance

preprint2020arXivOpen access

We prove Gaussian fluctuation for pair counting statistics of the form $\sum_{1\leq i\neq j\leq N} f(θ_i-θ_j)$ for the Circular Unitary Ensemble (CUE) of random matrices in the case of a slowly growing variance in the limit of large $N.$

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A note on pair dependent linear statistics with slowly growing variance

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