The speed of biased random walk on percolation clusters

Abstract

We consider biased random walk on supercritical percolation clusters in $\Z^2$. We show that the random walk is transient and that there are two speed regimes: If the bias is large enough, the random walk has speed zero, while if the bias is small enough, the speed of the random walk is positive.

This is a corrected version where the result is only proved for percolation clusters on Z^2; 23 Pages, 3 Figures