Central limit theorem for branching random walks in random environment

• 成果类型: Article
• 署名作者: Yoshida, Nobuo
• 署名单位: Kyoto University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/07-AAP500
• 发表日期: 2008
• 页码: 1619-1635
• 关键词: directed polymers; diffusion

摘要

We consider branching random walks in d-dimensional integer lattice with time-space i.i.d. offspring distributions. When d > 3 and the fluctuation of the environment is well moderated by the random walk, we prove a central limit theorem for the density of the population, together with upper bounds for the density of the most populated site and the replica overlap. We also discuss the phase transition of this model in connection with directed polymers in random environment.