2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171480We 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.29 pagesProbabilityAnalysis of PDEs60G50; 31C25text