Transience of percolation clusters on wedges

Abstract

We study random walks on supercritical percolation clusters on wedges in ${\mathbb{Z}}^3$, 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.

17 pages

Cited by in corpus (1)

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