ANALYTICAL APPROXIMATIONS TO THE LOW-ORDER STATISTICS OF DARK-MATTER DISTRIBUTIONS

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.