LARGE-SCALE STRUCTURE STATISTICS - FINITE-VOLUME EFFECTS

We study finite volume effects on the count probability distribution function P-N(l) and the averaged Q-body correlations <(xi)over bar>(Q) (2 less than or equal to Q less than or equal to 5). These statistics are computed for cubic cells, of size l. We use as an example the case of the matter distribution of a CDM universe involving similar to 3.10(5) particles. The main effect of the finiteness of the sampled volume is to induce an abrupt cut-off on the function P-N(l) at large N. This clear signature makes an analysis of the consequences easy, and one can envisage a correction procedure. As a matter of fact, we demonstrate how an unfair sample can strongly affect the estimates of the functions <(xi)over bar>(Q) for Q greater than or equal to 3 (and decrease the measured zero of the two-body correlation function). We propose a method to correct for this artefact, or at least to evaluate the corresponding errors. We show that the correlations are systematically underestimated by direct measurements. We find that, once corrected, the statistical properties of this CDM universe appear compatible with the scaling relation S-Q = <(xi)over bar>(Q)/<(xi)over bar>(Q-1)(2) = constant with respect to scale, in the nonlinear regime; it was not the case with direct measurements. However, we note a deviation from scaling at scales close to the correlation length. It is probably due to the transition between the highly non-linear regime and the weakly correlated regime, where the functions SQ also seem to present a plateau. We apply the same procedure to simulations with HDM and white noise initial conditions, with similar results. Our method thus provides the first accurate measurement of the normalized skewness, S-3, and the normalized kurtosis, S-4, for three typical models of large scale structure formation in an expanding universe.