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Probability Theory and Related Fields

, Volume 116, Issue 2, pp 273–302 | Cite as

The problem of the most visited site in random environment

  • Yueyun Hu
  • Zhan Shi

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.

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Yueyun Hu
    • 1
  • Zhan Shi
    • 2
  1. 1.Laboratoire de Probabilités, Université Paris VI, 4 Place Jussieu, F-75252 Paris Cedex 05, France. e-mail: hu@proba.jussieu.frFR
  2. 2.L.S.T.A. – URA 1321, Université Paris VI, 4 Place Jussieu, F-75252 Paris Cedex 05, France. e-mail: shi@ccr.jussieu.frFR

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