Continuity for the Rate Function of the Simple Random Walk on Supercritical Percolation Clusters

Naoki Kubota ()
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Naoki Kubota: Nihon University

Journal of Theoretical Probability, 2020, vol. 33, issue 4, 1948-1973

Abstract: Abstract We consider the simple random walk on supercritical percolation clusters in the multidimensional cubic lattice. In this model, a quenched large deviation principle holds for the position of the random walk. Its rate function depends on the law of the percolation configuration, and the aim of this paper is to study the continuity of the rate function in the law. To do this, it is useful that the rate function is expressed by the so-called Lyapunov exponent, which is the asymptotic cost paid by the random walk for traveling in a landscape of percolation configurations. In this context, we first observe the continuity of the Lyapunov exponent in the law of the percolation configuration and then lift it to the rate function.

Keywords: Percolation; Random walk; Random environment; Large deviations; Lyapunov exponent; 60K37; 60F10 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-019-00936-7

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