Hj. Mo et al., ANALYTICAL APPROXIMATIONS TO THE LOW-ORDER STATISTICS OF DARK-MATTER DISTRIBUTIONS, Monthly Notices of the Royal Astronomical Society, 286(4), 1997, pp. 979-993
We show that in a hierarchical clustering model the low-order statisti
cs of the density and the peculiar velocity fields can all be modelled
semi-analytically for a given cosmology and an initial density pertur
bation power spectrum P(k). We present such models for the two-point c
orrelation function xi(r), the amplitude Q of the three-point correlat
ion function, the mean pairwise peculiar velocity [upsilon(12)(r)], th
e pairwise peculiar velocity dispersion [upsilon(12)(2)(r)], and the o
ne-point peculiar velocity dispersion [upsilon(1)(2)]. We test our mod
els against results derived from N-body simulations. These models allo
w us to understand in detail how these statistics depend on P(k) and c
osmological parameters. They can also help us to interpret, and maybe
correct for, sampling effects when these statistics are estimated from
observations. The dependence of the small-scale pairwise peculiar vel
ocity dispersion on rich clusters in the sample, for instance, can be
studied quantitatively. There are also significant implications for th
e reconstruction of the cosmic density field from measurements in reds
hift-space.