Electronic Journal of Probability

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

Jean-Dominique Deuschel and Ryoki Fukushima

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 25 (2020), paper no. 75, 28 pp.

Dates
Received: 24 May 2019
Accepted: 8 June 2020
First available in Project Euclid: 4 July 2020

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1593828036

Digital Object Identifier
doi:10.1214/20-EJP478

Subjects
Primary: 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

Rights
Creative Commons Attribution 4.0 International License.

Citation

Deuschel, Jean-Dominique; Fukushima, Ryoki. Quenched tail estimate for the random walk in random scenery and in random layered conductance II. Electron. J. Probab. 25 (2020), paper no. 75, 28 pp. doi:10.1214/20-EJP478. https://projecteuclid.org/euclid.ejp/1593828036


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