The harmonic-measure distribution function of a planar domain, and the Schottky-Klein prime function
Duration: 57 mins 49 secs
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About this item
| Description: |
Ward, L
Friday 13th September 2019 - 10:00 to 11:00 |
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| Created: | 2019-09-13 11:05 |
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| Collection: | The complex analysis toolbox: new techniques and perspectives |
| Publisher: | Isaac Newton Institute |
| Copyright: | Ward, L |
| Language: | eng (English) |
| Abstract: | The h-function or harmonic-measure distribution function h(r)=hΩ,z0(r) of a planar region Ω with respect to a basepoint z0 in Ω records the probability that a Brownian particle released from z0 first exits Ω within distance r of z0, for r>0. For simply connected domains Ω 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 ω(ζ,α) 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. |
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