THE VACANT SET OF TWO-DIMENSIONAL CRITICAL RANDOM INTERLACEMENT IS INFINITE

• 成果类型: Article
• 署名作者: Comets, Francis; Popov, Serguei
• 署名单位: Universite Paris Cite; Universidade Estadual de Campinas; Universite Paris Cite; Universidade Estadual de Campinas
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1177
• 发表日期: 2017
• 页码: 4752-4785
• 关键词: inequality

摘要

For the model of two-dimensional random interlacements in the critical regime (i.e., alpha = 1), we prove that the vacant set is a.s. infinite, thus solving an open problem from [Commun. Math. Phys. 343 (2016) 129-164]. Also, we prove that the entrance measure of simple random walk on annular domains has certain regularity properties; this result is useful when dealing with soft local times for excursion processes.