Abstract
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.
Citation
Ben Hambly. Martin Barlow. "Parabolic Harnack inequality and local limit theorem for percolation clusters." Electron. J. Probab. 14 1 - 26, 2009. https://doi.org/10.1214/EJP.v14-587
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