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2006 Transience of percolation clusters on wedges
Noam Berger, Itai Benjamini, Omer Angel, Yuval Peres
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Electron. J. Probab. 11: 655-669 (2006). DOI: 10.1214/EJP.v11-345

Abstract

We study random walks on supercritical percolation clusters on wedges in $Z^3$, and show that the infinite percolation cluster is (a.s.) transient whenever the wedge is transient. This solves a question raised by O. Häggström and E. Mossel. We also show that for convex gauge functions satisfying a mild regularity condition, the existence of a finite energy flow on $Z^2$ is equivalent to the (a.s.) existence of a finite energy flow on the supercritical percolation cluster. This answers a question of C. Hoffman.

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Noam Berger. Itai Benjamini. Omer Angel. Yuval Peres. "Transience of percolation clusters on wedges." Electron. J. Probab. 11 655 - 669, 2006. https://doi.org/10.1214/EJP.v11-345

Information

Accepted: 7 August 2006; Published: 2006
First available in Project Euclid: 31 May 2016

zbMATH: 1109.60062
MathSciNet: MR2242658
Digital Object Identifier: 10.1214/EJP.v11-345

Subjects:
Primary: 60J45

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