Electronic Journal of Probability

A Central Limit Theorem for Random Walk in a Random Environment on a Marked Galton-Watson Tree.

Gabriel Faraud

Full-text: Open access

Abstract

Models of random walks in a random environment were introduced at first by Chernoff in 1967 in order to study biological mechanisms. The original model has been intensively studied since then and is now well understood. In parallel, similar models of random processes in a random environment have been studied. In this article we focus on a model of random walk on random marked trees, following a model introduced by R. Lyons and R. Pemantle (1992). Our point of view is a bit different yet, as we consider a very general way of constructing random trees with random transition probabilities on them. We prove an analogue of R. Lyons and R. Pemantle's recurrence criterion in this setting, and we study precisely the asymptotic behavior, under restrictive assumptions. Our last result is a generalization of a result of Y. Peres and O. Zeitouni (2006) concerning biased random walks on Galton-Watson trees.

Article information

Source
Electron. J. Probab., Volume 16 (2011), paper no. 6, 174-215.

Dates
Accepted: 12 January 2011
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464820175

Digital Object Identifier
doi:10.1214/EJP.v16-851

Mathematical Reviews number (MathSciNet)
MR2754802

Zentralblatt MATH identifier
1228.60115

Subjects
Primary: 60K37: Processes in random environments
Secondary: 60F05: Central limit and other weak theorems 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
Random Walk random environment tree branching random walk central limit theorem

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Faraud, Gabriel. A Central Limit Theorem for Random Walk in a Random Environment on a Marked Galton-Watson Tree. Electron. J. Probab. 16 (2011), paper no. 6, 174--215. doi:10.1214/EJP.v16-851. https://projecteuclid.org/euclid.ejp/1464820175


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