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

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

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


This is the third in a series of papers in which we consider one-dimensional RandomWalk 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.

Original languageEnglish
Pages (from-to)967-1009
Number of pages43
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Issue number2
StatePublished - May 2022


  • Cooling regimes
  • Dynamic random environment
  • Mixed fluctuations
  • Random walk
  • Recurrence versus transience
  • Refreshing times


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