The zero-one law for planar random walks in i.i.d. random environments revisited

2007/06/05 by Martin Zerner, Martin P. W. Zerner, Zerner, Martin P. W.
Biochemistry, Genetics and Molecular Biology · Decision Sciences · Mathematics · #Diffusion and Search Dynamics #FOS: Mathematics #Primary 60K37 #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics #math.PR #msc:60F20. #msc:60K37 #secondary 60F20.

paper · pdf · doi:10.48550/arxiv.0706.0745

9 pages

arxiv created 2007/06/05 · openalex publication_date 2007/06/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we present a simplified proof of the zero-one law by Merkl and Zerner (2001) for directional transience of random walks in i.i.d. random environments (RWRE) on the square lattice. Also, we indicate how to construct a two-dimensional counterexample in a non-uniformly elliptic and stationary environment which has better ergodic properties than the example given by Merkl and Zerner.

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