## The Annals of Probability

### 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 $d\geq4$. 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.

#### Article information

Source
Ann. Probab., Volume 44, Number 4 (2016), 2889-2979.

Dates
Revised: June 2015
First available in Project Euclid: 2 August 2016

https://projecteuclid.org/euclid.aop/1470139157

Digital Object Identifier
doi:10.1214/15-AOP1038

Mathematical Reviews number (MathSciNet)
MR3531683

Zentralblatt MATH identifier
1351.60132

#### Citation

Berger, Noam; Cohen, Moran; Rosenthal, Ron. Local limit theorem and equivalence of dynamic and static points of view for certain ballistic random walks in i.i.d. environments. Ann. Probab. 44 (2016), no. 4, 2889--2979. doi:10.1214/15-AOP1038. https://projecteuclid.org/euclid.aop/1470139157

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