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SUMMARY:The harmonic-measure distribution function of a planar domain\, an
 d the Schottky-Klein prime function - Lesley Ward (University of South Aus
 tralia)
DTSTART:20190913T090000Z
DTEND:20190913T100000Z
UID:TALK129547@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The $h$-function or harmonic-measure distribution function $h(
 r) = h_{\\Omega\, z_0}(r)$ of a planar region $\\Omega$ with respect to a 
 basepoint $z_0$ in $\\Omega$ records the probability that a Brownian parti
 cle released from $z_0$ first exits $\\Omega$ within distance $r$ of $z_0$
 \, for $r &gt\; 0$. For simply connected domains $\\Omega$ the theory of $
 h$-functions is now well developed\, and in particular the $h$-function ca
 n 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 ho
 w the Schottky-Klein prime function $\\omega(\\zeta\,\\alpha)$ allows us t
 o compute the $h$-function explicitly\, for a model class of multiply conn
 ected domains. This is joint work with Darren Crowdy\, Christopher Green\,
  and Marie Snipes.
LOCATION:Seminar Room 1\, Newton Institute
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