Disconnection, random walks, and random interlacements

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• 作者：Alain-Sol Sznitman
• 关键词：Mathematics Subject Classification60F10 ; 60K35 ; 60J27 ; 82B43
• 刊名：Probability Theory and Related Fields
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：167
• 期：1-2
• 页码：1-44
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Probability Theory and Stochastic Processes; Theoretical, Mathematical and Computational Physics; Quantitative Finance; Mathematical and Computational Biology; Statistics for Business/Economics/Mathem
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-2064
• 卷排序：167

文摘

We consider random interlacements on \({\mathbb {Z}}^d\), \(d\ge 3\), 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 \(d \ge 3\).