Asymptotic directions in random walks in random environment revisited

2009/02/06 by Alexander Drewitz, Drewitz, Alexander, Alejandro F. Ramı́rez +2
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #60F15 #60K37 #Bayesian Methods and Mixture Models #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60F15 #msc:60K37

paper · pdf · doi:10.48550/arxiv.0902.1115

arxiv created 2009/02/06 · openalex publication_date 2009/02/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently Simenhaus proved that for any elliptic random walk in random environment, transience in the neighborhood of a given direction is equivalent to the a.s. existence of a deterministic asymptotic direction and to transience in any direction in the open half space defined by this asymptotic direction. Here we prove an improved version of this result and review some open problems.

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