The Annals of Probability

On the transient (T) condition for random walk in mixing environment

Enrique Guerra Aguilar

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Abstract

We prove a ballistic strong law of large numbers and an invariance principle for random walks in strong mixing environments, under condition $(T)$ of Sznitman (cf. Ann. Probab. 29 (2001) 724–765). This weakens for the first time Kalikow’s ballisticity assumption on mixing environments and proves the existence of arbitrary finite order moments for the approximate regeneration time of F. Comets and O. Zeitouni (Israel J. Math. 148 (2005) 87–113). The main technical tool in the proof is the introduction of renormalization schemes, which had only been considered for i.i.d. environments.

Article information

Source
Ann. Probab., Volume 47, Number 5 (2019), 3003-3054.

Dates
Received: February 2018
Revised: November 2018
First available in Project Euclid: 22 October 2019

Permanent link to this document
https://projecteuclid.org/euclid.aop/1571731443

Digital Object Identifier
doi:10.1214/18-AOP1330

Mathematical Reviews number (MathSciNet)
MR4021243

Subjects
Primary: 60K37: Processes in random environments
Secondary: 82D30: Random media, disordered materials (including liquid crystals and spin glasses)

Keywords
Random walk in random environment ballisticity conditions strong mixing environments

Citation

Guerra Aguilar, Enrique. On the transient (T) condition for random walk in mixing environment. Ann. Probab. 47 (2019), no. 5, 3003--3054. doi:10.1214/18-AOP1330. https://projecteuclid.org/euclid.aop/1571731443


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