Prof. Dr. Frank den Hollander, Universität Leiden Holland, Vortrag: Extremal geometry of a Brownian porous medium
Thursday, 23.01.2014 16:30 im Raum M5
Abstract: The path $W[0,t]$ of a Brownian motion on a $d$-dimensional
torus $T^d$ run for time $t$ is a random compact subset of
$T^d$. In this talk we look at the geometric properties of
the complement $C(t) = T^d\W[0,t]$ as $t\to\infty$ for
$d\geq 3$. Questions we address are the following:
1. What is the linear size of the largest region in $C(t)$?
2. What does $C(t)$ look like around this region?
3. Does $C(t)$ have some sort of `component-structure'?
4. What are the largest capacity, largest volume and smallest
principal Dirichlet eigenvalue of the components of $C(t)?
We speculate about what happens for $d=2$, which is much
harder to understand.
Joint work with Jesse Goodman (Haifa)