ALMOST SURE CENTRAL LIMIT THEOREM FOR BRANCHING RANDOM WALKS IN RANDOM ENVIRONMENT

• 成果类型: Article
• 署名作者: Nakashima, Makoto
• 署名单位: Kyoto University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/10-AAP699
• 发表日期: 2011
• 页码: 351-373
• 关键词: linear stochastic evolutions; directed polymers; localization; diffusion; disorder

摘要

We consider the branching random walks in d-dimensional integer lattice with time-space i.i.d. offspring distributions. Then the normalization of the total population is a nonnegative martingale and it almost surely converges to a certain random variable. When d >= 3 and the fluctuation of environment satisfies a certain uniform square integrability then it is nondegenerate and we prove a central limit theorem for the density of the population in terms of almost sure convergence.