Many visits to a single site by a transient random walk in random environment.
The authors consider a transient random walk on \(Z\) in random environments and study the almost sure asymptotics of the supremum of its local time. The main result states that if the random walk has zero speed, there is a random sequence of sites and a random sequence of times such that the walk spends a positive fraction of the times at these sites. The method of proof relies on the connection of random walk in random environment with branching processes in random environment used by \textit{H.\ Kesten, M. V. Kozlov} and \textit{F. Spitzer} [Compos. Math. 30, 145--168 (1975; Zbl 0388.60069)].
scientific article; zbMATH DE number 2138967