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Parabolic Harnack inequality and local limit theorem for percolation clusters

Ben Hambly, Martin Barlow
2009 Electronic Journal of Probability  
We consider the random walk on supercritical percolation clusters in 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.
doi:10.1214/ejp.v14-587 fatcat:a5m7xpds2vdffn4q3dq524vhvi