ON THE UNIQUENESS OF THE INFINITE CLUSTER OF THE VACANT SET OF RANDOM INTERLACEMENTS

• 成果类型: Article
• 署名作者: Teixeira, Augusto
• 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: 10.1214/08-AAP547
• 发表日期: 2009
• 页码: 454-476
• 关键词: area

摘要

We consider the model of random interlacements on Z(d) introduced in Sznitman [Vacant set of random interlacements and percolation (2007) preprint]. For this model, we prove the uniqueness of the infinite component of the vacant set. As a consequence, we derive the continuity in a of the probability that the origin belongs to the infinite component of the vacant set at level a in the supercritical phase u < u*.