How universal are asymptotics of disconnection times in discrete cylinders?

• 成果类型: Article
• 署名作者: Sznitman, Alain-Sol
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117907000000114
• 发表日期: 2008
• 页码: 1-53
• 关键词: random-walks

摘要

We investigate the disconnection time of a simple random walk in a discrete cylinder with a large finite connected base. In a recent article of A. Dembo and the author it was found that for large N the disconnection time of G(N) x Z has rough order vertical bar GN vertical bar(2), when G(N) = (Z/NZ)(d). In agreement with a conjecture by I. Benjamini, we show here that this behavior has broad generality when the bases of the discrete cylinders are large connected graphs of uniformly bounded degree.