## The Annals of Probability

### A Zero-One Law for Planar Random walks in Random Environment

#### Abstract

We solve the problem posed by S.A. Kalikow whether the event that the $x$-coordinate of a random walk in a two-dimensional random environment approaches $\infty$ has necessarily probability either zero or one. The answer is yes if we assume the environment to be i.i.d.and in general no if we allow the environment to be just stationary and ergodic.

#### Article information

Source
Ann. Probab., Volume 29, Number 4 (2001), 1716-1732.

Dates
First available in Project Euclid: 5 March 2002

https://projecteuclid.org/euclid.aop/1015345769

Digital Object Identifier
doi:10.1214/aop/1015345769

Mathematical Reviews number (MathSciNet)
MR1880239

Zentralblatt MATH identifier
1016.60093

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

#### Citation

Zerner, Martin P. W.; Merkl, Franz. A Zero-One Law for Planar Random walks in Random Environment. Ann. Probab. 29 (2001), no. 4, 1716--1732. doi:10.1214/aop/1015345769. https://projecteuclid.org/euclid.aop/1015345769