HIERARCHICAL CORRELATIONS IN MODELS OF GALAXY CLUSTERING

We present a comparison of the predictions of perturbation theory for the hierarchical J-order correlation amplitudes S-J=($) over bar xi(J) /($) over bar xi(2)(J-1), J=3-10, with the results of large numerical simulations of gravitational clustering. We consider two different ini tial power spectra of density fluctuations, one being flatter than the other. The clustering amplitudes S-J measured in these models are dif ferent at all scales. In each case, the perturbation theory prediction s give an excellent agreement with the simulations on scales for which the variance is approximately linear, i.e. scales for which ($) over bar xi(2) less than or similar to 1. For cells of radius R greater tha n or similar to 30 h(-1) Mpc, the sampling variance arising from the f inite size of our simulations dominates the results. We also find that the S-J are roughly independent of time, Omega and lambda, as expecte d. On comparing with the observations, one can use these results to di scriminate between models for structure formation.