Quenched invariance principle for simple random walk on clusters in correlated percolation models
Probability
2015-09-28 v3 Combinatorics
Abstract
We prove quenched invariance principle for simple random walk on the unique infinite percolation cluster for a general class of percolation models on Z^d, d>=2, with long-range correlations introduced in arXiv:1212.2885, solving one of the open problems from there. This gives new results for random interlacements in dimension d>=3 at every level, as well as for the vacant set of random interlacements and the level sets of the Gaussian free field in the regime of the so-called local uniqueness (which is believed to coincide with the whole supercritical regime). An essential ingredient of our proof is a new isoperimetric inequality for correlated percolation models.
Keywords
Cite
@article{arxiv.1310.4764,
title = {Quenched invariance principle for simple random walk on clusters in correlated percolation models},
author = {Eviatar Procaccia and Ron Rosenthal and Artem Sapozhnikov},
journal= {arXiv preprint arXiv:1310.4764},
year = {2015}
}