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).

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Dates et versions

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

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