Parabolic Harnack Inequality and Local Limit Theorem for Percolation Clusters
Probability
2008-10-15 v1 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.0810.2467,
title = {Parabolic Harnack Inequality and Local Limit Theorem for Percolation Clusters},
author = {Martin Barlow and Ben Hambly},
journal= {arXiv preprint arXiv:0810.2467},
year = {2008}
}
Comments
29 pages