Electronic Journal of Probability

Precise large deviations for random walk in random environment

Dariusz Buraczewski and Piotr Dyszewski

Full-text: Open access

Abstract

We study one-dimensional nearest neighbour random walk in site-dependent random environment. We establish precise (sharp) large deviations in the so-called ballistic regime, when the random walk drifts to the right with linear speed. In the sub-ballistic regime, when the speed is sublinear, we describe the precise probability of slowdown.

Article information

Source
Electron. J. Probab., Volume 23 (2018), paper no. 114, 26 pp.

Dates
Received: 13 March 2018
Accepted: 25 October 2018
First available in Project Euclid: 23 November 2018

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1542942365

Digital Object Identifier
doi:10.1214/18-EJP239

Mathematical Reviews number (MathSciNet)
MR3885547

Zentralblatt MATH identifier
07021670

Subjects
Primary: 60K37: Processes in random environments 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
random walk in random environment large deviations branching process with immigration

Rights
Creative Commons Attribution 4.0 International License.

Citation

Buraczewski, Dariusz; Dyszewski, Piotr. Precise large deviations for random walk in random environment. Electron. J. Probab. 23 (2018), paper no. 114, 26 pp. doi:10.1214/18-EJP239. https://projecteuclid.org/euclid.ejp/1542942365


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