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We present a detailed comparison of the predictions of perturbation theory (PT) for the averaged J-point correlation functions, |J|, with the results of numerical simulations of gravitational clustering. We carry out a systematic analysis of this method using ensembles of simulations with different numbers of particles, different box sizes, and different particle arrangements and clustering amplitudes in the initial conditions. We estimate |J|, for J=2-10, from moments of counts in cells. We find significant non-linear effects in the variance, J=2, even at scales as large as |R30 h^-1| Mpc. Perturbation theory gives remarkable agreement at large scales, where |₂1|, with the measured hierarchical amplitudes |SJ=J/^J-1₂|. We follow the evolution of |J| in time and find that, at large scales, |R~7 h^-1| Mpc, at least during the last three expansion factors, the |SJ| do not change with time, which is as predicted by PT theory, despite the fact that the |J| have evolved by large factors, | 10^J-1|. We illustrate how these results can be applied to interpret the clustering in galaxy surveys and conclude that the observed hierarchical pattern in the APM Survey is compatible with gravitational evolution in unbiased, initially Gaussian, models.
Baugh et al. (Thu,) studied this question.