Quenched invariance principle for simple random walk on percolation clusters

Quenched invariance principle for simple random walk on percolation clusters

We consider the simple random walk on the (unique) infinite cluster of supercritical bond percolation in Z with d ≥ 2. We prove that, for almost every percolation configuration, the path distribution of the walk converges weakly to that of non-degenerate, isotropic Brownian motion. Our analysis is based on the consideration of a harmonic deformation of the infinite cluster on which the random w...

Quenched Invariance Principle for Simple Random Walk on Percolation Clusters

We consider the simple random walk on the (unique) infinite cluster of super-critical percolation in Z with d ≥ 2. We prove that, for almost every percolation configuration, the path distribution of the walk converges weakly to that of non-degenerate Brownian motion.

Quenched Invariance Principle for Simple Random Walk on Two-dimensional Percolation Clusters

We consider the simple random walk on a two-dimensional super-critical infinite percolation cluster. We prove that, for almost every percolation configuration, the path distribution of the walk converges weakly to a non-degenerate Brownian motion.

Quenched invariance principles for random walks on percolation clusters

We prove the almost sure (’quenched’) invariance principle for a random walker on an infinite percolation cluster in Z, d ≥ 2.

Scaling limit of simple random walk on supercritical percolation clusters