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
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. olle 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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