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2011 A Central Limit Theorem for Random Walk in a Random Environment on a Marked Galton-Watson Tree.
Gabriel Faraud
Author Affiliations +
Electron. J. Probab. 16: 174-215 (2011). DOI: 10.1214/EJP.v16-851

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.

Citation

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Gabriel Faraud. "A Central Limit Theorem for Random Walk in a Random Environment on a Marked Galton-Watson Tree.." Electron. J. Probab. 16 174 - 215, 2011. https://doi.org/10.1214/EJP.v16-851

Information

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

zbMATH: 1228.60115
MathSciNet: MR2754802
Digital Object Identifier: 10.1214/EJP.v16-851

Subjects:
Primary: 60K37
Secondary: 60F05 , 60J80

Keywords: Branching random walk , central limit theorem , random environment , Random walk , tree

Vol.16 • 2011
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