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November 2019 Heavy Bernoulli-percolation clusters are indistinguishable
Pengfei Tang
Ann. Probab. 47(6): 4077-4115 (November 2019). DOI: 10.1214/19-AOP1354

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 (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.

Citation

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Pengfei Tang. "Heavy Bernoulli-percolation clusters are indistinguishable." Ann. Probab. 47 (6) 4077 - 4115, November 2019. https://doi.org/10.1214/19-AOP1354

Information

Received: 1 September 2018; Revised: 1 March 2019; Published: November 2019
First available in Project Euclid: 2 December 2019

zbMATH: 07212178
MathSciNet: MR4038049
Digital Object Identifier: 10.1214/19-AOP1354

Subjects:
Primary: 60K35, 82B43
Secondary: 60B99, 60C05

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 6 • November 2019
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