Aggregation in a one-dimensional stochastic gas model with finite polynomial moments of particle speeds

Abstract

We consider a one-dimensional system of auto-gravitating sticky particles with random initial speeds and describe the process of aggregation in terms of the largest cluster size Ln at any fixed time prior to the critical time. We study the asymptotic behavior of Ln for the warm gas, i.e., for a system of particles with nonzero initial speeds vi(0) = ui, where (ui) is a family of i.i.d. random variables with mean zero, unit variance, and finite pth moment E(|ui|p) < ∞, p ≥ 2, and obtain sharp lower and upper bounds for Ln(t). Bibliography: 17 titles.