Solidification Estimates for Random Walks on Supercritical Percolation Clusters

We consider the simple random walk on the infinite cluster of a general class of percolation models on Zd, d≥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 Nitzschner and Sznitman (J. Eur.Math. Soc. (JEMS) 22(8), 2629–2672, 2020) for Brownian motion in Rd and in Chiarini and Nitzschner (Comm. Math. Phys. 386(3), 1685–1745, 2021) for random walks on Zd equipped with uniformly elliptic edge weights to a manifestly non-elliptic framework.