English

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

Probability 2025-03-04 v4

Abstract

In this paper, we study random walks evolving on Z in a dynamic random environment that we assume to have time correlations that decrease polynomially fast. We show a law of large numbers by generalizing methods already used for the nearest-neighbor framework to the finite-range one. This requires some new ideas to get around the absence of a monotonicity property that was crucial in the proof for the nearest-neighbour case. Our proof works both in discrete and continuous time.

Keywords

Cite

@article{arxiv.2304.03143,
  title  = {Law of large numbers for a finite-range random walk in a dynamic random environment with nonuniform mixing},
  author = {Julien Allasia},
  journal= {arXiv preprint arXiv:2304.03143},
  year   = {2025}
}

Comments

30 pages, 5 figures