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We consider the random walk on supercritical percolation clusters in thed-dimensional Euclidean lattice. Previous papers have obtained Gaussian heatkernel bounds, and a.s. invariance principles for this process. We show howthis information leads to a parabolic Harnack inequality, a local limit theoremand estimates on the Green's function.

Parabolic Harnack Inequality and Local Limit Theorem for Percolation Clusters