Functional central limit theorem for a random walk in a random environment

• 成果类型: Article
• 署名作者: Piau, D
• 署名单位: Universite Claude Bernard Lyon 1
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1998
• 页码: 1016-1040
• 关键词: galton-watson trees; speed

摘要

The simple random walk on a supercritical Galton-Watson tree is transient when the tree is infinite. Moreover, there exist regeneration times, that is, times when the walk crosses an edge for the first and the last time. We prove that the distance and the range of the walk satisfy functional central limit theorems under the annealed law GP. This result is a consequence of estimates of the law of the first regeneration time tau(R). We show that there exist positive c, c', alpha and beta such that, for all n greater than or equal to 1, exp(-cn(alpha)) less than or equal to GP[tau(R) greater than or equal to n] less than or equal to exp(-c' n(beta)).