Comptes Rendus
Complex Analysis/Mathematical Physics
Random curves by conformal welding
Comptes Rendus. Mathématique, Volume 348 (2010) no. 5-6, pp. 257-262.

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.

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.

Published online:
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
     author = {Kari Astala and Peter Jones and Antti Kupiainen and Eero Saksman},
     title = {Random curves by conformal welding},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {257--262},
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     year = {2010},
     doi = {10.1016/j.crma.2009.12.014},
     language = {en},
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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.

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Cited by 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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