The Annals of Applied Probability

Quenched limits for the fluctuations of transient random walks in random environment on $\mathbb{Z}$

Nathanaël Enriquez, Christophe Sabot, Laurent Tournier, and Olivier Zindy

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Abstract

We consider transient nearest-neighbor random walks in random environment on $\mathbb{Z}$. For a set of environments whose probability is converging to 1 as time goes to infinity, we describe the fluctuations of the hitting time of a level $n$, around its mean, in terms of an explicit function of the environment. Moreover, their limiting law is described using a Poisson point process whose intensity is computed. This result can be considered as the quenched analog of the classical result of Kesten, Kozlov and Spitzer [Compositio Math. 30 (1975) 145–168].

Article information

Source
Ann. Appl. Probab., Volume 23, Number 3 (2013), 1148-1187.

Dates
First available in Project Euclid: 7 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1362684857

Digital Object Identifier
doi:10.1214/12-AAP867

Mathematical Reviews number (MathSciNet)
MR3076681

Zentralblatt MATH identifier
1279.60126

Subjects
Primary: 60K37: Processes in random environments 60F05: Central limit and other weak theorems 82B41: Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]
Secondary: 60E07: Infinitely divisible distributions; stable distributions 60E10: Characteristic functions; other transforms

Keywords
Random walk in random environment quenched distribution Poisson point process fluctuation theory for random walks Beta distributions

Citation

Enriquez, Nathanaël; Sabot, Christophe; Tournier, Laurent; Zindy, Olivier. Quenched limits for the fluctuations of transient random walks in random environment on $\mathbb{Z}$. Ann. Appl. Probab. 23 (2013), no. 3, 1148--1187. doi:10.1214/12-AAP867. https://projecteuclid.org/euclid.aoap/1362684857


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