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July 2016 Local limit theorem and equivalence of dynamic and static points of view for certain ballistic random walks in i.i.d. environments
Noam Berger, Moran Cohen, Ron Rosenthal
Ann. Probab. 44(4): 2889-2979 (July 2016). DOI: 10.1214/15-AOP1038

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.

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Noam Berger. Moran Cohen. Ron Rosenthal. "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 (4) 2889 - 2979, July 2016. https://doi.org/10.1214/15-AOP1038

Information

Received: 1 August 2014; Revised: 1 June 2015; Published: July 2016
First available in Project Euclid: 2 August 2016

zbMATH: 1351.60132
MathSciNet: MR3531683
Digital Object Identifier: 10.1214/15-AOP1038

Subjects:
Primary: 60K37, 82D30

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 4 • July 2016
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