Clustering in a stochastic model of one-dimensional gas

• 成果类型: Article
• 署名作者: Vysotsky, Vladislav V.
• 署名单位: Saint Petersburg State University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/07-AAP481
• 发表日期: 2008
• 页码: 1026-1058
• 关键词: large-scale structure; conservation-laws; brownian-motion; DYNAMICS; universe; CONVERGENCE; diffusion; adhesion; systems; rates

摘要

We give a quantitative analysis of clustering in a stochastic model of one-dimensional gas. At time zero, the gas consists of n identical particles that are randomly distributed on the real line and have zero initial speeds. Particles begin to move under the forces of mutual attraction. When particles collide, they stick together forming a new particle, called cluster, whose mass and speed are defined by the laws of conservation. We are interested in the asymptotic behavior of K-n(t) as n -> infinity, where K-n(t) denotes the number of clusters at time t in the system with n initial particles. Our main result is a functional limit theorem for K-n(t). Its proof is based on the discovered localization property of the aggregation process, which states that the behavior of each particle is essentially defined by the motion of neighbor particles.