Parabolic Harnack inequality and local limit theorem for percolation clusters

Ben M Hambly (University of Oxford)
Martin T Barlow (University of British Columbia)


We consider the random walk on supercritical percolation clusters in $\mathbb{Z}^d$. 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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Pages: 1-26

Publication Date: January 7, 2009

DOI: 10.1214/EJP.v14-587


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