The problem of the most visited site in random environment
For the definition of a random walk in random environment (RWRE) see e. g. the book of \textit{P. Révész} [``Random walk in random and non-random environments'' (1990; Zbl 0733.60091)]. The authors prove that the most visited site of Sinai's simple random walk in random environment is transient. The method also applies to a class of recurrent diffusion processes with random potentials. For related papers see: \textit{M. Csörgő}, \textit{L. Horváth} and \textit{P. Révész} [Stochastic Processes Appl. 25, 185-202 (1987; Zbl 0634.60062)]; the authors and \textit{M. Yor} [Trans. Am. Math. Soc. 351, No.~10, 3915-3934 (1999; Zbl 0932.60083)]; and \textit{H. Kesten} [Physica A 138, 299-309 (1986; Zbl 0666.60065)].
scientific article; zbMATH DE number 1439657