Electronic Journal of Probability

Arbitrary many walkers meet infinitely often in a subballistic random environment

Alexis Devulder, Nina Gantert, and Françoise Pène

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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
Received: 30 November 2018
Accepted: 17 July 2019
First available in Project Euclid: 18 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1568793794

Digital Object Identifier
doi:10.1214/19-EJP344

Zentralblatt MATH identifier
07107384

Subjects
Primary: 60K37: Processes in random environments 60G50: Sums of independent random variables; random walks

Keywords
random walk random environment collisions recurrence transience

Rights
Creative Commons Attribution 4.0 International License.

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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