## Electronic Journal of Probability

### Arbitrary many walkers meet infinitely often in a subballistic random environment

#### Abstract

We consider $d$ independent walkers in the same random environment in $\mathbb{Z}$. 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 $d$ is — the $d$ walkers meet infinitely often, i.e. there are almost surely infinitely many times for which all the random walkers are at the same location.

#### Article information

Source
Electron. J. Probab., Volume 24 (2019), paper no. 100, 25 pp.

Dates
Accepted: 17 July 2019
First available in Project Euclid: 18 September 2019

https://projecteuclid.org/euclid.ejp/1568793794

Digital Object Identifier
doi:10.1214/19-EJP344

#### Citation

Devulder, Alexis; Gantert, Nina; Pène, Françoise. Arbitrary many walkers meet infinitely often in a subballistic random environment. Electron. J. Probab. 24 (2019), paper no. 100, 25 pp. doi:10.1214/19-EJP344. https://projecteuclid.org/euclid.ejp/1568793794

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