Dvoretzky, Erdős and Kakutani (1958) and Le Gall (1987) proved the existence of points that are visited infinitely often by two-dimensional Brownian motion. I am going to make elementary discussions on such points, by exploiting some ideas originating from the study of branching random walks. Work in progress with Elie Aïdékon and Yueyun Hu.
Zhan Shi is a Professor at Université Pierre et Marie Curie, Paris - France. His research interests include spatial branching processes and random walks.