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SUMMARY:Critical exponents in FK-weighted planar maps - Ray\, G (Universit
 y of British Columbia)
DTSTART:20150420T143000Z
DTEND:20150420T153000Z
UID:TALK59145@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:Co-authors: Nathanael Berestycki (University of Cambridge)\, B
 enoit Laslier (University of Cambridge) \n\nIn this paper we consider rand
 om planar maps weighted by the self-dual Fortuin--Kastelyn model with para
 meter q in (0\,4). Using a bijection due to Sheffield and a connection to 
 planar Brownian motion in a cone we obtain rigorously the value of critica
 l exponents associated with the length of cluster interfaces\, which is sh
 own to be\n$$rac{4}{pi} arccosleft(rac{ qrt{2- qrt{q}}}{2}\night).$$\nSi
 milar results are obtained for the area. Applying the KPZ formula we find 
 that this value is consistent with the dimension of SLE curves and SLE dua
 lity. Various isoperimetric relationships of independent interest are also
  derived.\n
LOCATION:Seminar Room 1\, Newton Institute
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