Solidification estimates for random walks on supercritical percolation clusters

Abstract

We consider the simple random walk on the infinite cluster of a general class of percolation models on ${\mathbb{Z}}^d$, $d\ge 3$, including Bernoulli percolation as well as models with strong, algebraically decaying correlations. For almost every realization of the percolation configuration, we obtain uniform controls on the absorption probability of a random walk by certain "porous interfaces" surrounding the discrete blow-up of a compact set $A$. These controls substantially generalize previous results obtained in arXiv:1706.07229 for Brownian motion in ${\mathbb{R}}^d$ and in arXiv:2012.05230 for random walks on ${\mathbb{Z}}^d$ equipped with uniformly elliptic edge weights to a manifestly non-elliptic framework.

42 pages, 2 figures, to appear in Potential Analysis