## Electronic Journal of Probability

### Precise large deviations for random walk in random environment

#### 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
Accepted: 25 October 2018
First available in Project Euclid: 23 November 2018

https://projecteuclid.org/euclid.ejp/1542942365

Digital Object Identifier
doi:10.1214/18-EJP239

Mathematical Reviews number (MathSciNet)
MR3885547

Zentralblatt MATH identifier
07021670

#### 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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