Open Access
2023 Transience and anchored isoperimetric dimension of supercritical percolation clusters
Tom Hutchcroft
Author Affiliations +
Electron. J. Probab. 28: 1-15 (2023). DOI: 10.1214/23-EJP905


We establish several equivalent characterisations of the anchored isoperimetric dimension of supercritical clusters in Bernoulli bond percolation on transitive graphs. We deduce from these characterisations together with a theorem of Duminil-Copin, Goswami, Raoufi, Severo, and Yadin (Duke Math. J. 2020) that if G is a transient transitive graph then the infinite clusters of Bernoulli percolation on G are transient for p sufficiently close to 1. It remains open to extend this result down to the critical probability. Along the way we establish two new cluster repulsion inequalities that are of independent interest.


We thank Russ Lyons his careful reading and helpful comments on an earlier version of this manuscript and thank Philip Easo for catching several typos.


Download Citation

Tom Hutchcroft. "Transience and anchored isoperimetric dimension of supercritical percolation clusters." Electron. J. Probab. 28 1 - 15, 2023.


Received: 22 September 2022; Accepted: 15 January 2023; Published: 2023
First available in Project Euclid: 20 January 2023

MathSciNet: MR4536689
zbMATH: 1515.60316
MathSciNet: MR4529085
Digital Object Identifier: 10.1214/23-EJP905

Primary: 60J99 , 60K35

Keywords: finite clusters , Isoperimetry , percolation , Random walk

Vol.28 • 2023
Back to Top