Martin Barlow, Ben Hambly
Published 2008-10-14Version 1
We consider the random walk on supercritical percolation clusters in the d-dimensional Euclidean lattice. Previous papers have obtained Gaussian heat kernel bounds, and a.s. invariance principles for this process. We show how this information leads to a parabolic Harnack inequality, a local limit theorem and estimates on the Green's function.
Local limit theorem for the maximum of a random walk
On Mukhin's necessary and sufficient condition for the validity of the local limit theorem
A local limit theorem for random walks on the chambers of $\tilde{A}_2$ buildings
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