The two regimes of moderate deviations for the range of a transient walk - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Probability Theory and Related Fields Année : 2021

The two regimes of moderate deviations for the range of a transient walk

Résumé

We obtain sharp upper and lower bounds for the downward moderate deviations of the volume of the range of a random walk in dimension five and larger. Our results encompass two regimes: a Gaussian regime for small deviations, and a stretched exponential regime for larger deviations. In the latter regime, we show that conditioned on the moderate deviations event, the walk folds a small part of its range in a ball-like subset. Also, we provide new path properties, in dimension three as well. Besides the key role Newtonian capacity plays in this study, we introduce two original ideas, of general interest, which strengthen the approach developed in [AS17].
Fichier principal
Vignette du fichier
range-rev.PTRF.pdf (318.68 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03759500 , version 1 (24-08-2022)

Identifiants

Citer

Amine Asselah, Bruno Schapira. The two regimes of moderate deviations for the range of a transient walk. Probability Theory and Related Fields, 2021, ⟨10.1007/s00440-021-01063-3⟩. ⟨hal-03759500⟩
24 Consultations
18 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More