Comptes Rendus
no. 5-6
Complex Analysis/Mathematical Physics
Random curves by conformal welding
[Courbes aléatoires par soudure conforme]

Présenté par : Paul Malliavin

Kari Astala1 ; Peter Jones2 ; Antti Kupiainen1 ; Eero Saksman1
1 University of Helsinki, Department of Mathematics and Statistics, P.O. Box 68, 00014 University of Helsinki, Finland
2 Department of Mathematics, Yale University, 10 Hillhouse Ave, New Haven, CT 06510, USA
Comptes Rendus. Mathématique, Volume 348 (2010) no. 5-6, pp. 257-262.

On construit une famille aléatoire conformément invariante de courbes fermées dans le plan par soudure d'un cercle unité donné en terme d'exponentielle d'un champ libre gaussien. On conjecture que nos courbes sont localement reliées à SLE(κ) pour κ<4.

We construct a conformally invariant random family of closed curves in the plane by welding of random homeomorphisms of the unit circle given in terms of the exponential of Gaussian Free Field. We conjecture that our curves are locally related to SLE(κ) for κ<4.

Reçu le :
Publié le :
DOI : 10.1016/j.crma.2009.12.014
Kari Astala 1 ; Peter Jones 2 ; Antti Kupiainen 1 ; Eero Saksman 1

1 University of Helsinki, Department of Mathematics and Statistics, P.O. Box 68, 00014 University of Helsinki, Finland
2 Department of Mathematics, Yale University, 10 Hillhouse Ave, New Haven, CT 06510, USA 
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Kari Astala; Peter Jones; Antti Kupiainen; Eero Saksman. Random curves by conformal welding. Comptes Rendus. Mathématique, Volume 348 (2010) no. 5-6, pp. 257-262. doi : 10.1016/j.crma.2009.12.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.12.014/

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Cité par Sources :

☆ We thank M. Bauer, D. Bernard, S. Rohde and S. Smirnov for discussions and L. Dubois for help in French.

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