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

被引：0
作者：
Naoki Kubota
机构：
[1] Nihon University,College of Science and Technology
来源：
Journal of Theoretical Probability | 2020年 / 33卷
关键词：
Percolation; Random walk; Random environment; Large deviations; Lyapunov exponent; 60K37; 60F10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：1948 / 1973
页数：25
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