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

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1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Keywords : Galton-Watson tree Random walk in random environment law of large numbers large deviations Galton-Watson tree.

Autor: Elie Aidekon -

Fuente: https://hal.archives-ouvertes.fr/

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