Abstract
Let {Ltz} be the jointly continuous local times of a one-dimensional Brownian motion and let Lt∗=supz∈RLtz. Let Vt be any point z such that Ltz=Lt∗, a most visited site of Brownian motion. We prove that if γ>1, then lim inft→∞ |Vt| t∕(logt)γ=∞,a.s., with an analogous result for simple random walk. This proves a conjecture of Lifshits and Shi.
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