Comptes Rendus
Probability theory/Mathematical physics
Convergence of Ising interfaces to Schrammʼs SLE curves
Comptes Rendus. Mathématique, Volume 352 (2014) no. 2, pp. 157-161.

We show how to combine our earlier results to deduce strong convergence of the interfaces in the planar critical Ising model and its random-cluster representation to Schrammʼs SLE curves with parameters κ=3 and κ=16/3, respectively.

Cet article explique comment combiner certains résultats antérieurs des différents auteurs afin de montrer la convergence forte des interfaces du modèle dʼIsing critique planaire et de sa représentation FK vers les courbes SLE(3) et SLE(16/3) introduites par Schramm.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.12.002

Dmitry Chelkak 1, 2; Hugo Duminil-Copin 3; Clément Hongler 4; Antti Kemppainen 5; Stanislav Smirnov 1, 3

1 Chebyshev Laboratory, Department of Mathematics and Mechanics, St. Petersburg State University, Russian Federation
2 St. Petersburg Department of Steklov Mathematical Institute (PDMI RAS), Russian Federation
3 Section de Mathématiques, Université de Genève, Switzerland
4 Department of Mathematics, Columbia University, United States
5 Department of Mathematics and Statistics, University of Helsinki, Finland
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Dmitry Chelkak; Hugo Duminil-Copin; Clément Hongler; Antti Kemppainen; Stanislav Smirnov. Convergence of Ising interfaces to Schrammʼs SLE curves. Comptes Rendus. Mathématique, Volume 352 (2014) no. 2, pp. 157-161. doi : 10.1016/j.crma.2013.12.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.12.002/

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