The heavy range of randomly biased walks on trees

Abstract : We focus on recurrent random walks in random environment (RWRE) on Galton-Watson trees. The range of these walks, that is the number of sites visited at some fixed time, has been studied in three different papers [AC18], [AdR17] and [dR16]. Here we study the heavy range: the number of edges visited at least α times for some real α. The asymptotic behavior of this process when α is a power of the number of steps of the walk is given for all the recurrent cases. It turns out that this heavy range plays a crucial role in the rate of convergence of an estimator of the environment from a single trajectory of the RWRE.
Type de document :
Pré-publication, Document de travail
34 pages (version 2). 2018
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Contributeur : Pierre Andreoletti <>
Soumis le : lundi 5 novembre 2018 - 09:37:17
Dernière modification le : mercredi 7 novembre 2018 - 01:16:21

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  • HAL Id : hal-01849187, version 2
  • ARXIV : 1811.02226

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Pierre Andreoletti, Roland Diel. The heavy range of randomly biased walks on trees. 34 pages (version 2). 2018. 〈hal-01849187v2〉

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