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A quenched central limit theorem for biased random walks on supercritical Galton–Watson trees
Part of
Adam Bowditch
Journal:

Journal of Applied Probability / Volume 55 / Issue 2 / June 2018

Published online by Cambridge University Press:

26 July 2018, pp. 610-626

Print publication:

June 2018
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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.

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