Heavy Bernoulli-percolation clusters are indistinguishable
Probability
2019-08-27 v2
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.
Keywords
Cite
@article{arxiv.1809.01284,
title = {Heavy Bernoulli-percolation clusters are indistinguishable},
author = {Pengfei Tang},
journal= {arXiv preprint arXiv:1809.01284},
year = {2019}
}