Critical branching Brownian motion with absorption: survival probability

• 成果类型: Article
• 署名作者: Berestycki, Julien; Berestycki, Nathanael; Schweinsberg, Jason
• 署名单位: Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Cambridge; University of California System; University of California San Diego
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0533-9
• 发表日期: 2014
• 页码: 489-520
• 关键词: random-walk; traveling-waves; absorbing wall; laplacian; BOUNDARY

摘要

We consider branching Brownian motion on the real line with absorption at zero, in which particles move according to independent Brownian motions with the critical drift of -root 2. Kesten (Stoch Process 7:9-47, 1978) showed that almost surely this process eventually dies out. Here we obtain upper and lower bounds on the probability that the process survives until some large time t. These bounds improve upon results of Kesten (Stoch Process 7:9-47, 1978), and partially confirm nonrigorous predictions of Derrida and Simon (EPL 78: 60006, 2007).