Large deviations for simple random walk on percolations with long-range correlations
Probability
2013-11-04 v2
Abstract
We show quenched large deviations for the simple random walk on a certain class of percolations with long-range correlations. This class contains the supercritical Bernoulli percolations, the model considered by Drewitz, R'ath and Sapozhnikov and the random-cluster model up to the slab critical point. Our result is an extension of Kubota's result for the supercritical Bernoulli percolations. We also state a shape theorem for the chemical distance, which is an extension of Garet and Marchand's result for the supercritical Bernoulli percolations.
Cite
@article{arxiv.1308.2282,
title = {Large deviations for simple random walk on percolations with long-range correlations},
author = {Kazuki Okamura},
journal= {arXiv preprint arXiv:1308.2282},
year = {2013}
}
Comments
12 pages, New theorem added