Transience of percolation clusters on wedges

Noam Berger (University of California, Los Angeles)
Itai Benjamini (The Weizmann Institute)
Omer Angel (University of British Columbia)
Yuval Peres (The University of California, Berkeley)


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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Pages: 655-669

Publication Date: August 7, 2006

DOI: 10.1214/EJP.v11-345


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