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.
"Transience of percolation clusters on wedges." Electron. J. Probab. 11 655 - 669, 2006. https://doi.org/10.1214/EJP.v11-345