Asymptotic direction of a ballistic random walk in a two-dimensional random environment with nonuniform mixing

2023/07/04 by Julien Allasia, Allasia, Julien
Biochemistry, Genetics and Molecular Biology · Mathematics · #Diffusion and Search Dynamics #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2307.01603

openalex publication_date 2023/07/04 · openalex created_date 2023/07/07 · openalex updated_date 2026/07/28

Abstract

In this paper, we study random walks evolving with a directional bias in a two-dimensional random environment with correlations that vanish polynomially. Using renormalization methods first employed for one-dimensional dynamic environments along with additional ideas specific to this new framework, we show that there exists an asymptotic direction for such a random walk. We also provide examples of classical models for which our results apply.

Citations

• Sharpness of the phase transition for continuum percolation in R²
• Fluctuation bounds for symmetric random walks on dynamic environments via Russo-Seymour-Welsh

Cited by

• Law of large numbers for a finite-range random walk in a dynamic random environment with nonuniform mixing

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