On the most visited sites of planar Brownian motion

Valentina Cammarota, Peter Mörters

Let (B_t : t > 0) be a planar Brownian motion and define gauge functions ${\varphi }_{\alpha }(s)=log(1/s{)}^{-\alpha }$ for $\alpha >0$. If $\alpha <1$ we show that almost surely there exists a point x in the plane s…