Abstract:Année de publication : 1999
Perturbation Theory (PT) applied to a cosmological density field with Gaussian initial fluctuations suggests a specific hierarchy for the correlation functions when the variance is small. In particular quantitative predictions have been made for the moments and the shape of the one-point probability distribution function (PDF) of the top-hat smoothed density. In this paper we perform a series of systematic checks of these predictions against N-body computations both in 2D and 3D with a wide range of featureless power spectra. In agreement with previous studies, we found that the reconstructed PDF-s work remarkably well down to very low probabilities, even when the variance approaches unity. Our results for 2D reproduce the features for the 3D dynamics. In particular we found that the PT predictions are more accurate for spectra with less power on small scales. In highly nonlinear regime, on the other hand, different assumptions regarding amplitudes of different tree topologies contributing to higher order correlation functions lead to specific predictions regarding the scaling properties of Void Probability Function (VPF) and Count Probability Distribution Function (CPDF). However most efforts to determine these amplitudes from dynamical theory of gravitational clustering has lead to over simplification of BBGKY equations at highly nonlinear regime. Generic predictions regarding VPF and CPDF were made assuming that these amplit\ udes can be constructed from multiplicative nature of vertex amplitudes appearing in tree level approximation of correlation hierarchy. We test these predictions against simulations in 2D and\ 3D and determine the unknown parameters which appear due to lack of complete knowledge of all hierarchal amplitudes. These studies have been done with unprecedented dynamical range, especially for the 2D case, allowing in particular more robust determination of the asymptotic behavior of the VPF confirming scaling arguments. We have introduced a new method to determine the moments based on the factorial moments for efficient subtraction of Poisson noise from discrete data. Based on scaling properties we propose a new method for correcting finite volume effect in determination of higer order correlation functions. Results of analysis using this method are presented.