Heavy Bernoulli-percolation clusters are indistinguishable

2018/09/05 by Tang, Pengfei · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1809.01284

Abstract

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 (1999) in the Bernoulli percolation case and confirms a conjecture of Schonmann (2001). We also prove that every infinite cluster of Bernoulli percolation on a nonamenable quasi-transitive graph is transient almost surely.

Cited by

• Heavy repulsion of clusters in Bernoulli percolation

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