Abstract for the talk at 14.05.2013 (15:15 h)Oberseminar ANALYSIS - PROBABILITY
Jesse Goodman (Universiteit Leiden)
The gaps left by a Brownian motion
Run a Brownian motion on a torus for a long time. How large are the random gaps left behind when the path is removed? In three or more dimensions, we find that there is a deterministic spatial scale common to all the large gaps anywhere in the torus. Moreover, we can identify whether a gap of a given shape is likely to exist on this scale, in terms of a single parameter, the classical (Newtonian) capacity. I will describe why this allows us to identify a well-defined "component" structure in our random porous set. Based on joint work with Frank den Hollander.