THE Λ-COALESCENT SPEED OF COMING DOWN FROM INFINITY

• 成果类型: Article
• 署名作者: Berestycki, Julien; Berestycki, Nathanael; Limic, Vlada
• 署名单位: Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Cambridge; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP475
• 发表日期: 2010
• 页码: 207-233
• 关键词: INEQUALITIES

摘要

Consider a Lambda-coalescent that comes down from infinity (meaning that it starts from a configuration containing infinitely many blocks at time 0, yet it has a finite number N-t of blocks at any positive time t > 0). We exhibit a deterministic function v: (0, infinity) -> (0, infinity) such that N-t/v(t) -> 1, almost surely, and in L-p for any p >= 1, as t -> 0. Our approach relies on a novel martingale technique.