Limit of the environment viewed from Sinaï's walk - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2023

Limit of the environment viewed from Sinaï's walk

Résumé

For Sinai's walk we show that the empirical measure of the environment seen from the particle converges in law to some random measure. This limit measure is explicitly given in terms of the infinite valley, which construction goes back to Golosov (1984). As a consequence an "in law" ergodic theorem holds. When the limit is deterministic, it holds in probability. This allows some extensions to the recurrent case of the ballistic "environment's method" dating back to Kozlov and Molchanov (1984).
Fichier principal
Vignette du fichier
Dev_short_15.08.23--.pdf (328.76 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03914411 , version 1 (02-10-2023)

Identifiants

Citer

Francis Comets, Oleg Loukianov, Dasha Loukianova. Limit of the environment viewed from Sinaï's walk. 2023. ⟨hal-03914411⟩
24 Consultations
12 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More