Large deviations for random walks in random environment on a Galton-Watson tree

Details Large deviations for random walks in random environment on a Galton-Watson tree Large deviations for random walks in random environment on a Galton-Watson tree

2008-11-04

arxiv.org/abs/0811.0438v1

Ann. I.H.P. Prob. Stat. , Vol. 46, Number 1 (2010), 159-189

Mathematics

Probability

Scientific paper

10.1214/09-AIHP204

Consider a random walk in random environment on a supercritical Galton--Watson tree, and let $\tau_n$ be the hitting time of generation $n$. The paper presents a large deviation principle for $\tau_n/n$, both in quenched and annealed cases. Then we investigate the subexponential situation, revealing a polynomial regime similar to the one encountered in one dimension. The paper heavily relies on estimates on the tail distribution of the first regeneration time.

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