COVER LEVELS AND RANDOM INTERLACEMENTS

• 成果类型: Article
• 署名作者: Belius, David
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/11-AAP770
• 发表日期: 2012
• 页码: 522-540
• 关键词: random-walk; discrete cylinders; vacant set; percolation; disconnection

摘要

This note investigates cover levels of finite sets in the random interlacements model introduced in [Ann. of Math. (2) 171 (2010) 2039-2087], that is, the least level such that the set is completely contained in the random interlacement at that level. It proves that as the cardinality of a set goes to infinity, the resealed and recentered cover level tends in distribution to the Gumbel distribution with cumulative distribution function exp(-exp(-z)).