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Quenched Limit Theorems for Nearest Neighbour Random Walks in 1D Random Environment

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Abstract

It is well known that random walks in a one dimensional random environment can exhibit subdiffusive behavior due to the presence of traps. In this paper we show that the passage times of different traps are asymptotically independent exponential random variables with parameters forming, asymptotically, a Poisson process. This allows us to prove weak quenched limit theorems in the subdiffusive regime where the contribution of traps plays the dominating role.

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Authors and Affiliations

  1. Department of Mathematics and Institute of Physical Science and Technology, University of Maryland, College Park, MD, 20742, USA

    D. Dolgopyat

  2. School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, Great Britain

    I. Goldsheid

Authors
  1. D. Dolgopyat
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  2. I. Goldsheid
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Correspondence to I. Goldsheid.

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Communicated by F. L. Toninelli

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Dolgopyat, D., Goldsheid, I. Quenched Limit Theorems for Nearest Neighbour Random Walks in 1D Random Environment. Commun. Math. Phys. 315, 241–277 (2012). https://doi.org/10.1007/s00220-012-1539-3

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  • DOI: https://doi.org/10.1007/s00220-012-1539-3

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