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

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

Published:2018-06 Issue:2 Volume:55 Page:610-626
ISSN:0021-9002
Container-title:Journal of Applied Probability
language:en
Short-container-title:J. Appl. Probab.

Author:

Bowditch Adam

Abstract

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.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Reference13 articles.

1. A central limit theorem for biased random walks on Galton–Watson trees

2. Slowdown estimates and central limit theorem for random walks in random environment

3. On the static and dynamic points of view for certain random walks in random environment;Bolthausen;Meth. Appl. Anal.,2002

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