Convergence of Ising interfaces to Schrammʼs SLE curves

Chelkak, Dmitry; Duminil-Copin, Hugo; Hongler, Clément; Kemppainen, Antti; Smirnov, Stanislav

doi:10.1016/j.crma.2013.12.002

Probability theory/Mathematical physics

Convergence of Ising interfaces to Schrammʼs SLE curves
[Convergence des interfaces dʼIsing vers les courbes SLE introduites par Schramm]

Présenté par : the Editorial Board

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

Comptes Rendus. Mathématique, Tome 352 (2014) no. 2, pp. 157-161.

Résumé
Abstract

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.

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.

Reçu le : 2013-12-04
Accepté le : 2013-12-04
Publié le : 2014-01-04

DOI : 10.1016/j.crma.2013.12.002

Affiliations des auteurs :

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

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     title = {Convergence of {Ising} interfaces to {Schramm's} {SLE} curves},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {157--161},
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Chelkak, Dmitry; Duminil-Copin, Hugo; Hongler, Clément; Kemppainen, Antti; Smirnov, Stanislav. Convergence of Ising interfaces to Schrammʼs SLE curves. Comptes Rendus. Mathématique, Tome 352 (2014) no. 2, pp. 157-161. doi : 10.1016/j.crma.2013.12.002. http://www.numdam.org/articles/10.1016/j.crma.2013.12.002/

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