Integrability of exit times and ballisticity for random walks in Dirichlet environment

Abstract

We consider random walks in Dirichlet environment, introduced by Enriquez and Sabot in 2006. As this distribution on environments is not uniformly elliptic, the annealed integrability of exit times out of a given finite subset is a non-trivial property. We provide here an explicit equivalent condition for this integrability to happen, on general directed graphs. Such integrability problems arise for instance from the definition of Kalikow auxiliary random walk. Using our condition, we prove a refined version of the ballisticity criterion given by Enriquez and Sabot.

References in corpus (1)

• Random walks in random Dirichlet environment are transient in dimension $d\ge 3$

Cited by in corpus (11)

• Random walks in random Dirichlet environment are transient in dimension $d\ge 3$
• Random Dirichlet environment viewed from the particle in dimension $d\ge 3$
• Quenched exit estimates and ballisticity conditions for higher-dimensional random walk in random environment
• Sharp ellipticity conditions for ballistic behavior of random walks in random environment
• Effective Polynomial Ballisticity Condition for Random Walk in Random Environment
• A quenched invariance principle for non-elliptic random walk in i.i.d. balanced random environment
• Zero-one law for directional transience of one-dimensional random walks in dynamic random environments
• Ellipticity criteria for ballistic behavior of random walks in random environment
• Random Walks in Dirichlet Random Environments on $\mathbb{Z}$ with Bounded Jumps
• Random walk in random environment and their time-reversed counterpart
• Local trapping for elliptic random walks in random environments in ${\mathbb{Z}}^d$