English

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

Probability 2024-06-14 v2

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.

Keywords

Cite

@article{arxiv.2307.01603,
  title  = {Asymptotic direction of a ballistic random walk in a two-dimensional random environment with nonuniform mixing},
  author = {Julien Allasia},
  journal= {arXiv preprint arXiv:2307.01603},
  year   = {2024}
}