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The gaps left by Brownian motion on a torus

Mon 21 January 2013, 16:00

Jesse Goodman
University of Leiden

Analysis

Organiser: Michiel van den Berg

ABSTRACT
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.
Joint work with Frank den Hollander.