Parabolic Harnack Inequality and Local Limit Theorem for Percolation Clusters

Martin Barlow; Ben Hambly

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arXiv · 0810.2467

Parabolic Harnack Inequality and Local Limit Theorem for Percolation Clusters

Martin Barlow·Ben Hambly

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Abstract

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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Martin Barlow, Ben Hambly. 2008-10-14. Parabolic Harnack Inequality and Local Limit Theorem for Percolation Clusters. https://arxiv.org/abs/0810.2467

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