We have studied two-, three-, and four-point correlation functions using the cosmological N-body simulations aiming at quantifying their mutual relations. Particular attention was paid to see whether or not they obey the hierarchical clustering Ansatz which states that N-point correlation functions of cosmological gravitating systems are written down as N - 1 products of two-point correlation functions. In our analysis, different geometrical configurations of three and four points are treated separately, which enabled us to quantify for the first time configuration-dependent behavior of the correlations functions up to the fourth order. We found that the hierarchical clustering Ansatz holds only very approximately, and that there is clear evidence against the Ansatz especially in strongly nonlinear regimes of fluctuations. We discuss in detail how the departure from the Ansatz depends on the underlying fluctuation spectrum and the configurations of three and/or four points. The effect of peculiar velocity field makes the correlation functions in redshift space obey the hierarchical clustering Ansatz better than in real space. Thus a straightforward analysis of redshift surveys would lead to a misleading result in this sense.
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Suto et al. (1994) studied this question.