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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > The harmonic-measure distribution function of a planar domain, and the Schottky-Klein prime function

## The harmonic-measure distribution function of a planar domain, and the Schottky-Klein prime functionAdd to your list(s) Download to your calendar using vCal - Lesley Ward (University of South Australia)
- Friday 13 September 2019, 10:00-11:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact info@newton.ac.uk. CATW01 - The complex analysis toolbox: new techniques and perspectives The $h$-function or harmonic-measure distribution function $h® = h_{\Omega, z_0}(r)$ of a planar region $\Omega$ with respect to a basepoint $z_0$ in $\Omega$ records the probability that a Brownian particle released from $z_0$ first exits $\Omega$ within distance $r$ of $z_0$, for $r > 0$. For simply connected domains $\Omega$ the theory of $h$-functions is now well developed, and in particular the $h$-function can often be computed explicitly, making use of the Riemann mapping theorem. However, for multiply connected domains the theory of $h$-functions has been almost entirely out of reach. I will describe recent work showing how the Schottky-Klein prime function $\omega(\zeta,\alpha)$ allows us to compute the $h$-function explicitly, for a model class of multiply connected domains. This is joint work with Darren Crowdy, Christopher Green, and Marie Snipes. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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