1998/07/02 by Patrick Valageas, P. Valageas, Valageas, P.
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Astrophysics (astro-ph) #Complex Systems and Time Series Analysis #FOS: Physical sciences #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #astro-ph
paper · pdf · doi:10.48550/arxiv.astro-ph/9807033
17 pages, 4 figures To be published in A&A
arxiv created 1998/07/02 · openalex publication_date 1998/07/02 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Within the framework of hierarchical clustering we show that a simple Press-Schechter-like approximation, based on spherical dynamics, provides a good estimate of the evolution of the density field in the quasi-linear regime up to Σ∼ 1. Moreover, it allows one to recover the exact series of the cumulants of the probability distribution of the density contrast in the limit Σ→ 0 which sheds some light on the rigorous result and on ``filtering''. We also obtain similar results for the divergence of the velocity field. Next, we extend this prescription to the highly non-linear regime, using a stable-clustering approximation. Then we recover a specific scaling of the counts-in-cells which is indeed seen in numerical simulations, over a well-defined range. To this order we also introduce an explicit treatment of the behaviour of underdensities, which takes care of the normalization and is linked to the low-density bubbles and the walls one can see in numerical simulations. We compare this to a 1-dimensional adhesion model, and we present the consequences of our prescription for the power-law tail and the cutoff of the density distribution.