Sur la saucisse de Wiener et les points multiples du mouvement Brownien. (On the Wiener sausage and the multiple points of Brownian motion) (Q1090007)

The Wiener sausage is obtained by swelling the Brownian path, by expanding each point of the path to a ball of radius \(\epsilon\). This paper uses arguments about intersections and self-intersections of the Wiener sausage to establish results concerning the local time and Hausdorff measure of intersections and multiple points of the Brownian path. In particular, a conjecture of Taylor concerning the Hausdorff measure is established. A basic tool in establishing the required facts for the Wiener sausage is a set of asymptotics for Brownian hitting times. These are established using William's time-reversal representation of a diffusion.