Maher Boudabra, Greg Markowsky
Published 2020-01-23Version 1
In this paper we address the question of finding the point which maximizes the $p$-th moment of the exit time of planar Brownian motion from a given domain. We present a geometrical method of excluding parts of the domain from consideration which makes use of a coupling argument and the conformal invariance of Brownian motion. In many cases the maximizing point can be localized to a relatively small region. Several illustrative examples are presented.
On the finiteness of moments of the exit time of planar Brownian motion from comb domains
The exit time of planar Brownian motion and the Phragmen-Lindelof principle
Many proofs that $\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{π^2}{6}$ can be found in the conformal invariance of planar Brownian motion
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