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

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

doi:10.1214/21-aihp1184

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

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

Authors

Luca Avena

Yuki Chino

Dr Conrado Da Costa conrado.da-costa@durham.ac.uk
Assistant Professor

Frank den Hollander

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 of Mathematical Statistics
Peer Reviewed	Peer Reviewed
Volume	58
Issue	2
Pages	967-1009
DOI	https://doi.org/10.1214/21-aihp1184