Large deviations for simple random walk on percolations with long-range correlations

TL;DR

This paper establishes large deviation principles for simple random walks on percolation models with long-range correlations, extending previous results to broader classes including the random-cluster model.

Contribution

It extends quenched large deviation results and shape theorems to percolation models with long-range correlations, beyond classical Bernoulli percolation.

Findings

Proved quenched large deviations for a class of correlated percolation models.

Extended shape theorem for chemical distance to models with long-range correlations.

Included models such as the random-cluster model up to the slab critical point.

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.