Aggregation rates in one-dimensional stochastic systems with adhesion and gravitation

• 成果类型: Article
• 署名作者: Lifshits, M; Shi, Z
• 署名单位: Saint Petersburg State University; Universite Paris Cite; Sorbonne Universite; Universite de Lille
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000900
• 发表日期: 2005
• 页码: 53-81
• 关键词: mass aggregation; statistics; DYNAMICS; gas

摘要

We consider one-dimensional systems of self-gravitating sticky particles with random initial data and describe the process of aggregation in terms of the largest cluster size L-n at any fixed time prior to the critical time. The asymptotic behavior of L-n is also analyzed for sequences of times tending to the critical time. A phenomenon of phase transition shows up, namely, for small initial particle speeds (cold gas) L-n has logarithmic order of growth while higher speeds (warm gas) yield polynomial rates for L-n.