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.