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Preprints, Working Papers, ... Year : 2020

Maximal local time of randomly biased random walks on a Galton-Watson tree

Abstract

We consider a recurrent random walk on a rooted tree in random environment given by a branching random walk. Up to the first return to the root, its edge local times form a Multi-type Galton-Watson tree with countably infinitely many types. When the walk is the diffusive or sub-diffusive, by studying the maximal type of this Galton-Watson tree, we establish the asymptotic behaviour of the largest local times of this walk during n excursions, under the annealed law.
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Dates and versions

hal-02951423 , version 1 (28-09-2020)
hal-02951423 , version 2 (30-09-2020)

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Xinxin Chen, Loïc de Raphélis. Maximal local time of randomly biased random walks on a Galton-Watson tree. 2020. ⟨hal-02951423v2⟩
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