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Transience of percolation clusters on wedges

Omer Angel·Itai Benjamini·Noam Berger·Yuval Peres
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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. Haggstrom 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 solves a question of C. Hoffman.

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Omer Angel, Itai Benjamini, Noam Berger, Yuval Peres. 2002-06-12. Transience of percolation clusters on wedges. https://arxiv.org/abs/math/0206130

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