Neighboring clusters in Bernoulli percolation

• 成果类型: Article
• 署名作者: Timar, Adam
• 署名单位: Indiana University System; Indiana University Bloomington
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000485
• 发表日期: 2006
• 页码: 2332-2343
• 关键词: invariant percolation; transitions; graphs

摘要

We consider Bernoulli percolation on a locally finite quasi-transitive unimodular graph and prove that two infinite clusters cannot have infinitely many pairs of vertices at distance I from one another or, in other words, that such graphs exhibit cluster repulsion. This partially answers a question of Haggstrom, Peres and Schonmann.