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

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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

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

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

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

random walk random scenery spectral dimension random conductance model layered media

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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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