Geometric properties of 2-dimensional Brownian paths (Q1117593)

Let A be the set of all points of the plane \({\mathbb{C}}\), visited by 2- dimensional Brownian motion before time 1. With probability 1, all points of A are ``twist points'' except a set of harmonic measure zero. ``Twist points'' may be continuously approached in \({\mathbb{C}}\setminus A\) only along a special spiral. Although negligible in the sense of harmonic measure, various classes of ``cone points'' are dense in A, with probability 1. ``Cone points'' may be approached in \({\mathbb{C}}\setminus A\) within suitable wedges.