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Tracing the Filamentary Structure of the Galaxy Distribution at z~0.8

We study filamentary structure in the galaxy distribution at z ~ 0.8 using data from the Deep Extragalactic Evolutionary Probe 2 (DEEP2) Redshift Survey and its evolution to z ~ 0.1 using data from the Sloan Digital Sky Survey (SDSS). We trace individual filaments for both surveys using the Smoothed Hessian Major Axis Filament Finder, an algorithm which employs the Hessian matrix of the galaxy density field to trace the filamentary structures in the distribution of galaxies. We extract 33 subsamples from the SDSS data with a geometry similar to that of DEEP2. We find that the filament length distribution has not significantly changed since z ~ 0.8, as predicted in a previous study using a $\Lamda$CDM cosmological N-body simulation. However, the filament width distribution, which is sensitive to the non-linear growth of structure, broadens and shifts to smaller widths for smoothing length scales of 5-10 Mpc/h from z ~ 0.8 to z ~ 0.1, in accord with N-body simulations.