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September 2019 On the transient (T) condition for random walk in mixing environment
Enrique Guerra Aguilar
Ann. Probab. 47(5): 3003-3054 (September 2019). DOI: 10.1214/18-AOP1330

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.

Citation

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Enrique Guerra Aguilar. "On the transient (T) condition for random walk in mixing environment." Ann. Probab. 47 (5) 3003 - 3054, September 2019. https://doi.org/10.1214/18-AOP1330

Information

Received: 1 February 2018; Revised: 1 November 2018; Published: September 2019
First available in Project Euclid: 22 October 2019

zbMATH: 07145309
MathSciNet: MR4021243
Digital Object Identifier: 10.1214/18-AOP1330

Subjects:
Primary: 60K37
Secondary: 82D30

Keywords: ballisticity conditions , Random walk in random environment , strong mixing environments

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 5 • September 2019
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