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SUMMARY:Conformal invariance of boundary touching loops of FK Ising model 
 - Kemppainen\, A (University of Helsinki)
DTSTART:20150127T150000Z
DTEND:20150127T160000Z
UID:TALK57529@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-author: Stanislav Smirnov (University of Geneva and St. Pet
 ersburg State University) \n\nI will present a result showing the full con
 formal invariance of Fortuin-Kasteleyn representation of Ising model (FK I
 sing model) at criticality. The collection of all the interfaces\, which i
 n a planar model are closed loops\, in the FK Ising model at criticality d
 efined on a lattice approximation of a planar domain is shown to converge 
 to a conformally invariant scaling limit as the mesh size is decreased. Mo
 re specifically\, the scaling limit can be described using a branching SLE
 (?\,?-6) with ?=16/3\, a variant of Oded Schramm's SLE curves. We consider
  the exploration tree of the loop collection and the main step of the proo
 f is to find a discrete holomorphic observable which is a martingale for t
 he branch of the exploration tree. \n\nThis is a joint work with Stanislav
  Smirnov (University of Geneva and St. Petersburg State University)\n
LOCATION:Seminar Room 1\, Newton Institute
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