A Stationary, Mixing and Perturbative Counterexample to the 0-1-law for Random Walk in Random Environment in Two Dimensions

Mathematics – Probability

Scientific paper

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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.

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