The heavy range of randomly biased walks on trees - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2018

The heavy range of randomly biased walks on trees

Pierre Andreoletti
  • Fonction : Auteur
  • PersonId : 836997
  • IdRef : 076551245
Roland Diel

Résumé

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.
Fichier principal
Vignette du fichier
HRAD.pdf (522.4 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01849187 , version 1 (25-07-2018)
hal-01849187 , version 2 (05-11-2018)
hal-01849187 , version 3 (19-12-2018)

Identifiants

Citer

Pierre Andreoletti, Roland Diel. The heavy range of randomly biased walks on trees. 2018. ⟨hal-01849187v2⟩
221 Consultations
157 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More