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arXiv · 0811.0438

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

Elie Aidekon
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Abstract

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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Elie Aidekon. 2008-11-04. Large deviations for random walks in random environment on a Galton-Watson tree. https://doi.org/10.1214/09-aihp204

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