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Random Walks in Cooling Random Environments

  • Luca Avena
  • Frank den HollanderEmail author
Conference paper
  • 330 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 300)

Abstract

We propose a model of a one-dimensional random walk in dynamic random environment that interpolates between two classical settings: (I) the random environment is sampled at time zero only; (II) the random environment is resampled at every unit of time. In our model the random environment is resampled along an increasing sequence of deterministic times. We consider the annealed version of the model, and look at three growth regimes for the resampling times: (R1) linear; (R2) polynomial; (R3) exponential. We prove weak laws of large numbers and central limit theorems. We list some open problems and conjecture the presence of a crossover for the scaling behaviour in regimes (R2) and (R3).

Keywords

Random walk Dynamic random environment Resampling times Law of large numbers Central limit theorem 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Mathematical InstituteLeiden UniversityLeidenThe Netherlands

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