Structure of cosmic web in non-linear regime: the nearest neighbour and
  spherical contact distributions
  In non-linear scales, the matter density distribution is not Gaussian.
Consequently, the widely used two-point correlation function is not adequate
anymore to capture the matter density field's entire behaviour. Among all
statistics beyond correlation functions, the spherical contact (or equivalently
void function), and nearest neighbour distribution function seem promising
tools to probe matter distribution in non-linear regime. In this work, we use
halos from cosmological N-body simulations, galaxy groups from the
volume-limited galaxy group and central galaxies from mock galaxy catalogues,
to compare the spherical contact with the nearest neighbour distribution
functions. We also calculate the J-function (or equivalently the first
conditional correlation function), for different samples. Moreover, we consider
the redshift evolution and mass-scale dependence of statistics in the
simulations and dependence on the magnitude of volume-limited samples in group
catalogues as well as the mock central galaxies. The shape of the spherical
contact probability distribution function is nearly skew-normal, with skewness
and kurtosis being approximately 0.5 and 3, respectively. On the other hand,
the nearest neighbour probability distribution function is nearly log-normal,
with logarithmic skewness and kurtosis being approximately 0.1 and 2.5,
respectively. Accordingly, the spherical contact distribution function probes
larger scales compared to the nearest neighbour distribution function, which is
influenced by details of structures. We also find a linear relation between the
mean and variance of the spherical contact probability distribution function in
simulations and mock galaxies, which could be used as a distinguishing probe of
cosmological models.
