## The Annals of Probability

- Ann. Probab.
- Volume 16, Number 2 (1988), 722-729.

### A Zero or One Law for One Dimensional Random Walks in Random Environments

#### Abstract

We prove a zero or one law for one dimensional random walks in random environments for which the probability of making jumps of size $n$ decays exponentially. As an application we conclude that these random walks are recurrent if the distribution of the random environment is symmetric.

#### Article information

**Source**

Ann. Probab., Volume 16, Number 2 (1988), 722-729.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176991783

**Digital Object Identifier**

doi:10.1214/aop/1176991783

**Mathematical Reviews number (MathSciNet)**

MR929074

**Zentralblatt MATH identifier**

0642.60022

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60K99: None of the above, but in this section

Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

**Keywords**

Random walk in random environment zero or one law harmonic functions recurrence

#### Citation

Andjel, Enrique D. A Zero or One Law for One Dimensional Random Walks in Random Environments. Ann. Probab. 16 (1988), no. 2, 722--729. doi:10.1214/aop/1176991783. https://projecteuclid.org/euclid.aop/1176991783