The speed of biased random walk on percolation clusters
  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. 
Noam Berger, Nina Gantert, Yuval Peres