Random walk in cooling random environment: recurrence versus transience and mixed fluctuations

Avena, Luca; Chino, Yuki; da Costa, Conrado; den Hollander, Frank

Abstract

This is the third in a series of papers in which we consider one-dimensional Random Walk in Cooling Random Environment (RWCRE). The latter is obtained by starting from one-dimensional Random Walk in Random Environment (RWRE) and resampling the environment along a sequence of deterministic times, called refreshing times. In the present paper we explore two questions for general refreshing times. First, we investigate how the recurrence versus transience criterion known for RWRE changes for RWCRE. Second, we explore the fluctuations for RWCRE when RWRE is either recurrent or satisfies a classical central limit theorem. We show that the answer depends in a delicate way on the choice of the refreshing times. An overarching goal of our paper is to investigate how the behaviour of a random process with a rich correlation structure can be affected by resettings.

Citation

Avena, L., Chino, Y., da Costa, C., & den Hollander, F. (2022). Random walk in cooling random environment: recurrence versus transience and mixed fluctuations. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 58(2), 967-1009. https://doi.org/10.1214/21-aihp1184

• Journal Article Type: Article
• Acceptance Date: May 4, 2021
• Online Publication Date: May 15, 2022
• Publication Date: 2022
• Deposit Date: Nov 12, 2020
• Publicly Available Date: Jul 19, 2022
• Journal: Annales de l'Institut Henri Poincaré
• Print ISSN: 0246-0203
• Publisher: Institute Henri Poincaré
• Peer Reviewed: Peer Reviewed
• Volume: 58
• Issue: 2
• Pages: 967-1009
• DOI: https://doi.org/10.1214/21-aihp1184
• Public URL: https://durham-repository.worktribe.com/output/1257277