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


 
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1. Title Title of document A Central Limit Theorem for Random Walk in a Random Environment on a Marked Galton-Watson Tree.
 
2. Creator Author's name, affiliation, country Gabriel Faraud; Université Paris 13; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random Walk, random environment, tree, branching random walk, central limit theorem.
 
3. Subject Subject classification 60K37; 60F05; 60J80
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) ANR Project MEMEMO
 
7. Date (YYYY-MM-DD) 2011-01-12
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/851
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-851
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 16
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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