A COMPARISON OF THE EVOLUTION OF DENSITY FIELDS IN PERTURBATION-THEORY AND NUMERICAL SIMULATIONS .2. COUNTS-IN-CELLS ANALYSIS

We present a detailed comparison of the predictions of perturbation th eory (PT) for the averaged J-point correlation functions, <(xi)over ba r>(J), with the results of numerical simulations of gravitational clus tering. We carry out a systematic analysis of this method using ensemb les of simulations with different numbers of particles, different box sizes, and different particle arrangements and clustering amplitudes i n the initial conditions. We estimate <(xi)over bar>(J), for J = 2-10, from moments of counts in cells. We find significant non-linear effec ts in the variance, J = 2, even at scales as large as R similar to 30 h(-1) Mpc. Perturbation theory gives remarkable agreement at large sca les, where <(xi)over bar>(2) less than or similar to 1, with the measu red hierarchical amplitudes S-J = <(xi)over bar>(J)/<(xi)over bar>(J-1 )(2). We follow the evolution of <(xi)over bar>(J) in time and find th at, at large scales, R greater than or similar to 7 h(-1) Mpc, at leas t during the last three expansion factors, the S-J do not change with time, which is as predicted by PT theory, despite the fact that the <( xi)over bar>(J) have evolved by large factors, similar or equal to 10( J-1). We illustrate how these results can be applied to interpret the clustering in galaxy surveys and conclude that the observed hierarchic al pattern in the APM Survey is compatible with gravitational evolutio n in unbiased, initially Gaussian, models.