New Statistical Perspective to The Cosmic Void Distribution
  In this study, we obtain the size distribution of voids as a 3-parameter
redshift independent log-normal void probability function (VPF) directly from
the Cosmic Void Catalog (CVC). Although many statistical models of void
distributions are based on the counts in randomly placed cells, the log-normal
VPF that we here obtain is independent of the shape of the voids due to the
parameter-free void finder of the CVC. We use three void populations drawn from
the CVC generated by the Halo Occupation Distribution (HOD) Mocks which are
tuned to three mock SDSS samples to investigate the void distribution
statistically and the effects of the environments on the size distribution. As
a result, it is shown that void size distributions obtained from the HOD Mock
samples are satisfied by the 3-parameter log-normal distribution. In addition,
we find that there may be a relation between hierarchical formation, skewness
and kurtosis of the log-normal distribution for each catalog. We also show that
the shape of the 3-parameter distribution from the samples is strikingly
similar to the galaxy log-normal mass distribution obtained from numerical
studies. This similarity of void size and galaxy mass distributions may
possibly indicate evidence of nonlinear mechanisms affecting both voids and
galaxies, such as large scale accretion and tidal effects. Considering in this
study all voids are generated by galaxy mocks and show hierarchical structures
in different levels, it may be possible that the same nonlinear mechanisms of
mass distribution affect the void size distribution.
