Non-local scaling in two-dimensional gravitational clustering

Using an ensemble of high-resoluti on 2D numerical simulations, we explore the scaling properties of cosmological density fluctuations in the non-linear regime. We study the scaling behaviour of the usual N-point volume-averaged correlations, but also examine the scaling of the entire probability density function (PDF) of the fluctuations. We focus on two important issues: (i) whether the scaling behaviour of 2D clustering is consistent with what one infers from radial collapse arguments; and (ii) whether there is any evidence from these high-resolution simulations that a regime of stable clustering is ever entered. We find that the answers are (i) yes and (ii) no. We further find that the behaviour of the highly non-linear regime in these simulations suggests the existence of a regime in which the correlation function is independent of the initial power spectrum.