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A quenched central limit theorem for biased random walks on supercritical Galton–Watson trees

Part of: Markov processes Special processes Limit theorems

Published online by Cambridge University Press:  26 July 2018

Adam Bowditch
Adam Bowditch*
Affiliation:
University of Warwick
*
* Current address: Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore 119076. Email address: [email protected]
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Abstract

In this paper we prove a quenched functional central limit theorem for a biased random walk on a supercritical Galton–Watson tree with leaves. This extends a result of Peres and Zeitouni (2008) where the case without leaves was considered. A conjecture of Ben Arous and Fribergh (2016) suggests an upper bound on the bias which we observe to be sharp.

Keywords

Random walkrandom environmentGalton–Watson treefunctional central limit theoremquenchedinvariance principle

MSC classification

Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60K37: Processes in random environments 60F05: Central limit and other weak theorems 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 2 , June 2018 , pp. 610 - 626
Copyright
Copyright © Applied Probability Trust 2018 

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