Transience of a symmetric random walk in infinite measure

Timothée Bénard (1, 2)

1 ENS-PSL - École normale supérieure - Paris
2 UP11 - Université Paris-Sud - Paris 11

We consider a random walk on a second countable locally compact topological space endowed with an invariant Radon measure. We show that if the walk is symmetric and if every subset which is invariant by the walk has zero or infinite measure, then one has transience in law for almost every starting point. We then deduce a converse to Eskin-Margulis recurrence theorem.

Domaines: Systèmes dynamiques [math.DS]; Probabilités [math.PR]

Timothée Bénard. Transience of a symmetric random walk in infinite measure. 2021. ⟨hal-02845403v3⟩