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 integer 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
37 pages. 2018
Liste complète des métadonnées
Contributeur : Pierre Andreoletti <>
Soumis le : mercredi 19 décembre 2018 - 17:28:48
Dernière modification le : jeudi 17 janvier 2019 - 14:38:04


Fichiers produits par l'(les) auteur(s)


  • HAL Id : hal-01849187, version 3
  • ARXIV : 1811.02226


Pierre Andreoletti, Roland Diel. The heavy range of randomly biased walks on trees. 37 pages. 2018. 〈hal-01849187v3〉



Consultations de la notice


Téléchargements de fichiers