Parabolic Harnack Inequality and Local Limit Theorem for Percolation Clusters

Details Parabolic Harnack Inequality and Local Limit Theorem for Percolation Clusters Parabolic Harnack Inequality and Local Limit Theorem for Percolation Clusters

2008-10-14

arxiv.org/abs/0810.2467v1

Mathematics

Probability

29 pages

Scientific paper

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.

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