Random walks on supercritical percolation clusters

We obtain Gaussian upper and lower bounds on the transition density q(t)(x, y) of the continuous time simple random walk on a supercritical percolation cluster C(infinity) in the Euclidean lattice. The bounds, analogous to Aronsen's bounds for uniformly elliptic divergence form diffusions, hold with constants c(i) depending only on p (the percolation probability) and d. The irregular nature of the medium means that the bound for q(t) (x, (.)) holds only for t greater than or equal to S(x) (omega), where the constant S(x) (omega) depends on the percolation configuration omega.