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 $$\mathbb {Z}^d$$ Z d , $$d\ge 3$$ 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 $$\mathbb {R}^d$$ R d and in Chiarini and Nitzschner (Comm. Math. Phys. 386 (3), 1685–1745, 2021) for random walks on $$\mathbb {Z}^d$$ Z d equipped with uniformly elliptic edge weights to a manifestly non-elliptic framework.