# Drunks in an unfair world: Elliptic measures and the geometry of the domains

Zihui Zhao
Thursday, April 26, 2018 - 2:30pm to 3:20pm
PDL C-36
Abstract: Given a bounded domain $\Omega$, the harmonic measure $\omega$ is a probability measure on $\partial\Omega$ and it characterizes where a Brownian traveller in $\Omega$ is likely to exit the domain from. The elliptic measure is a non-homogenous variant of harmonic measure.
Since 1917, there has been much study about the relationship between $\omega$ and the surface measure $\sigma$ of the boundary. In particular, are $\omega$ and $\sigma$ absolutely continuous with each other? In this talk, I will show how a positive answer to this question implies that the corresponding domain enjoys good geometric property.
This talk is a preparation for my thesis defense!
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