Large deviations for occupation time profiles of random interlacements

• 成果类型: Article
• 署名作者: Li, Xinyi; 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/s00440-014-0550-3
• 发表日期: 2015
• 页码: 309-350
• 关键词: random-walk; vacant set

摘要

We derive a large deviation principle for the density profile of occupation times of random interlacements at a fixed level in a large box of , . As an application, we analyze the asymptotic behavior of the probability that atypically high values of the density profile insulate a macroscopic body in a large box. As a step in this program, we obtain a similar large deviation principle for the occupation-time measure of Brownian interlacements at a fixed level in a large box of , and we derive a new identity for the Laplace transform of the occupation-time measure, which is based on the analysis of certain Schrodinger semi-groups.