Quenched tail estimate for the random walk in random scenery and in random layered conductance. II. (English) Zbl 1505.60091

Deuschel, Jean-Dominique; Fukushima, Ryoki

Electron. J. Probab. 25, Paper No. 75, 28 p. (2020).

Summary: This is a continuation of our earlier work [Part I, Stochastic Processes Appl. 129, No. 1, 102–128 (2019; Zbl 1404.60037)] 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.

MSC:

60K37	Processes in random environments
60F10	Large deviations
60J55	Local time and additive functionals

Keywords:

random walk; random scenery; spectral dimension; random conductance model; layered media

Citations:

Zbl 1404.60037

References:

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