HEAVY BERNOULLI-PERCOLATION CLUSTERS ARE INDISTINGUISHABLE

• 成果类型: Article
• 署名作者: Tang, Pengfei
• 署名单位: Indiana University System; Indiana University Bloomington
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/19-AOP1354
• 发表日期: 2019
• 页码: 4077-4115
• 关键词: anchored expansion; infinite clusters; spectral-radius; random-walks; uniqueness; graphs

摘要

We prove that the heavy clusters are indistinguishable for Bernoulli percolation on quasi-transitive nonunimodular graphs. As an application, we show that the uniqueness threshold of any quasi-transitive graph is also the threshold for connectivity decay. This resolves a question of Lyons and Schramm (Ann. Probab.27 (1999) 1809-1836) in the Bernoulli percolation case and confirms a conjecture of Schonmann (Comm. Math. Phys. 219 (2001) 271-322). We also prove that every infinite cluster of Bernoulli percolation on a nonamenable quasi-transitive graph is transient almost surely.