UPPER BOUND ON THE DISCONNECTION TIME OF DISCRETE CYLINDERS AND RANDOM INTERLACEMENTS

• 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: 10.1214/09-AOP450
• 发表日期: 2009
• 页码: 1715-1746
• 关键词: local-times

摘要

We study the asymptotic behavior for large N of the disconnection time T(N) of a simple random walk on the discrete cylinder (Z/NZ)(d) x Z, when d >= 2. We explore its connection with the model of random interlacements on Z(d+1) recently introduced in [Ann. Math., in press], and specifically with the percolative properties of the vacant set left by random interlacements. As an application we show that in the large N limit the tail of T(N)/N(2d) is dominated by the tail of the first time when the supremum over the space variable of the Brownian local times reaches a certain critical value. As a by-product, we prove the tightness of the laws of T(N)/N(2d), when d >= 2.