Work

Infinitely many collisions between a recurrent simple random walk and arbitrary many transient random walks in a subballistic random environment

Year: 2025

Type: article

Abstract: We consider d random walks (Sn(j))n∈N, 1≤j≤d, in the same random environment ω in Z, and a recurrent simple random walk (Zn)n∈N on Z. We assume that, conditionally on the environment ω, all the random walks are independent and start from even initial locations. Our assumption on the law of the environment is such that a single random walk in the environment ω is transient to the right but subballistic, with parameter 0<κ<1∕2. We show that – for every value of d – there are almost surely infinitely many times for which all these random walks, (Zn)n∈N and (Sn(j))n∈N, 1≤j≤d, are simultaneously at the same location, even though one of them is recurrent and the d others ones are transient.

Source: Electronic Communications in Probability

DOI: 10.1214/25-ecp687

Author: Alexis Devulder

Institutions: Centre National de la Recherche Scientifique, Université de Versailles Saint-Quentin-en-Yvelines, Université Paris-Saclay, Laboratoire de Mathématiques de Versailles

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $675

OpenAlex ID: W4410236231