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The problem of the most visited site in random environment
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  • Published: February 2000

The problem of the most visited site in random environment

  • Yueyun Hu1 &
  • Zhan Shi2 

Probability Theory and Related Fields volume 116, pages 273–302 (2000)Cite this article

Abstract.

We prove that the process of the most visited site of Sinai's simple random walk in random environment is transient. The rate of escape is characterized via an integral criterion. Our method also applies to a class of recurrent diffusion processes with random potentials. It is interesting to note that the corresponding problem for the usual symmetric Bernoulli walk or for Brownian motion remains open.

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Authors and Affiliations

  1. Laboratoire de Probabilités, Université Paris VI, 4 Place Jussieu, F-75252 Paris Cedex 05, France. e-mail: hu@proba.jussieu.fr, , , , , , FR

    Yueyun Hu

  2. L.S.T.A. – URA 1321, Université Paris VI, 4 Place Jussieu, F-75252 Paris Cedex 05, France. e-mail: shi@ccr.jussieu.fr, , , , , , FR

    Zhan Shi

Authors
  1. Yueyun Hu
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  2. Zhan Shi
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Received: 17 April 1998

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Hu, Y., Shi, Z. The problem of the most visited site in random environment. Probab Theory Relat Fields 116, 273–302 (2000). https://doi.org/10.1007/PL00008730

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  • Issue Date: February 2000

  • DOI: https://doi.org/10.1007/PL00008730

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  • Mathematics Subject Classification (1991): 60J15, 60J60, 60J55, 60F15
  • Key words and phrases: Favourite site – local time – rate of escape – Sinai's random walk in random environment – diffusion with random potential
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