Convergence of Ising interfaces to Schrammʼs SLE curves

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

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

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

Comptes Rendus. Mathématique, Volume 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 :

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

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     author = {Dmitry Chelkak and Hugo Duminil-Copin and Cl\'ement Hongler and Antti Kemppainen and Stanislav Smirnov},
     title = {Convergence of {Ising} interfaces to {Schramm's} {SLE} curves},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {157--161},
     publisher = {Elsevier},
     volume = {352},
     number = {2},
     year = {2014},
     doi = {10.1016/j.crma.2013.12.002},
     language = {en},
}

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%A Antti Kemppainen
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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/

Bibliographie
Cité par

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