The gaps left by a Brownian motion

  • Jesse Goodman (Universiteit Leiden)
A3 01 (Sophus-Lie room)


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.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of This Seminar

  • Mar 12, 2024 tba with Theresa Simon
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