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