Transience of percolation clusters on wedges

Abstract

We study random walks on supercritical percolation clusters on wedges in ℤ3, 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 Z2 is equivalent to the (a.s.) existence of a finite energy flow on the supercritical percolation cluster. This answers a question of C. Hoffman. © 2006 Applied Probability Trust.