Quenched tail estimate for the random walk in random scenery and in random layered conductance II

Abstract

This is a continuation of our earlier work [Stochastic Processes and their Applications, 129(1), pp.102--128, 2019] on the random walk in random scenery and in random layered conductance. We complete the picture of upper deviation of the random walk in random scenery, and also prove a bound on lower deviation probability. Based on these results, we determine asymptotics of the return probability, a certain moderate deviation probability, and the Green function of the random walk in random layered conductance.

arXiv comment31 pages, 2 figures. Local central limit theorem and the Green function result are corrected. Some new remarks added

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Cited by in corpus (1)

• Quenched Invariance Principle for a class of random conductance models with long-range jumps