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

Julien Allasia

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arXiv · 2307.01603

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

Julien Allasia

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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.

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Julien Allasia. 2023-07-04. Asymptotic direction of a ballistic random walk in a two-dimensional random environment with nonuniform mixing. https://arxiv.org/abs/2307.01603

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