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.
