Conformal invariance of boundary touching loops of FK Ising model
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About this item
| Description: |
Kemppainen, A (University of Helsinki)
Tuesday 27 January 2015, 15:00-16:00 |
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| Created: | 2015-02-02 12:36 |
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| Collection: | Random Geometry |
| Publisher: | Isaac Newton Institute |
| Copyright: | Kemppainen, A |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | Co-author: Stanislav Smirnov (University of Geneva and St. Petersburg State University)
I will present a result showing the full conformal invariance of Fortuin-Kasteleyn representation of Ising model (FK Ising model) at criticality. The collection of all the interfaces, which in a planar model are closed loops, in the FK Ising model at criticality defined on a lattice approximation of a planar domain is shown to converge to a conformally invariant scaling limit as the mesh size is decreased. More 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 proof is to find a discrete holomorphic observable which is a martingale for the branch of the exploration tree. This is a joint work with Stanislav Smirnov (University of Geneva and St. Petersburg State University) |
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