## Electronic Journal of Probability

### A Stationary, mixing and perturbative counterexample to the 0-1-law for random walk in random environment in two dimensions

#### Abstract

We construct a two-dimensional counterexample of a random walk in random environment (RWRE). The environment is stationary, mixing and perturbative, and the corresponding RWRE has non trivial probability to wander off to the upper right. This is in contrast to the 0-1-law that holds for i.i.d. environments.

#### Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 1, 33 pp.

Dates
Accepted: 4 January 2013
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ejp/1465064226

Digital Object Identifier
doi:10.1214/EJP.v18-1880

Mathematical Reviews number (MathSciNet)
MR3024095

Zentralblatt MATH identifier
1286.60101

Subjects
Primary: 60F20: Zero-one laws
Secondary: 60K37: Processes in random environments

Rights

#### Citation

Heil, Hadrian. A Stationary, mixing and perturbative counterexample to the 0-1-law for random walk in random environment in two dimensions. Electron. J. Probab. 18 (2013), paper no. 1, 33 pp. doi:10.1214/EJP.v18-1880. https://projecteuclid.org/euclid.ejp/1465064226

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