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

2013/08/10 by Okamura, Kazuki
#60K35 #60K37 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1308.2282

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.

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