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Talk

The gaps left by a Brownian motion

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

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.

Based on joint work with Frank den Hollander.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

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