Local limit theorem and equivalence of dynamic and static points of view for certain ballistic random walks in i.i.d. environments

Abstract

In this work, we discuss certain ballistic random walks in random environments on ${\mathbb{Z}}^d$, and prove the equivalence between the static and dynamic points of view in dimension $d\ge 4$. Using this equivalence, we also prove a version of a local limit theorem which relates the local behavior of the quenched and annealed measures of the random walk by a prefactor.

Published at http://dx.doi.org/10.1214/15-AOP1038 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• An almost sure invariance principle for random walks in a space-time random environment
• The Point of View of the Particle on the Law of Large Numbers for Random Walks in a Mixing Random Environment

Cited by in corpus (1)

• Random walk on a perturbation of the infinitely-fast mixing interchange process