English

Arbitrary many walkers meet infinitely often in a subballistic random environment

Probability 2019-09-04 v2 Mathematical Physics math.MP

Abstract

We consider dd independent walkers in the same random environment in Z\mathbb{Z}. Our assumption on the law of the environment is such that a single walker is transient to the right but subballistic. We show that - no matter what dd is - the dd walkers meet infinitely often, i.e. there are almost surely infinitely many times for which all the random walkers are at the same location.

Keywords

Cite

@article{arxiv.1811.12763,
  title  = {Arbitrary many walkers meet infinitely often in a subballistic random environment},
  author = {Alexis Devulder and Nina Gantert and Françoise Pene},
  journal= {arXiv preprint arXiv:1811.12763},
  year   = {2019}
}

Comments

26 pages, 1 figure, to appear in Electronic Journal of Probability

R2 v1 2026-06-23T06:26:56.568Z