Disconnection, random walks, 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: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0676-y
• 发表日期: 2017
• 页码: 1-44
• 关键词: vacant set; large deviations; percolation; time

摘要

We consider random interlacements on Z(d), d >= 3, when their vacant set is in a strongly percolative regime. We derive an asymptotic upper bound on the probability that the random interlacements disconnect a box of large side-length from the boundary of a larger homothetic box. As a corollary, we obtain an asymptotic upper bound on a similar quantity, where the random interlacements are replaced by the simple random walk. It is plausible, but open at the moment, that these asymptotic upper bounds match the asymptotic lower bounds obtained by Xinyi Li and the author in (Electron. J. Probab. 19(17): 1-26, 2014), for random interlacements, and by Xinyi Li in (A lower bound on disconnection by simple random walk. arXiv: 1412.3959, 2014), for the simple random walk. In any case, our bounds capture the principal exponential rate of decay of these probabilities, in any dimension d >= 3.