Geodesic
Conformal loop ensembles: the Markovian characterization and the loop-soup construction
Scott Sheffield1 ; Wendelin Werner2
1 Department of Mathematics<br/> Massachusetts Institute of Technology<br/> 77 Massachusetts Ave.<br/> Cambridge, MA 02139
2 Laboratoire de Mathématiques<br/> Université Paris-Sud <br/> 91405 Orsay<br/> France<br/> and <br/> Ecole Normale Supérieure<br/> 75230 Paris<br/> France
Annals of mathematics, Tome 176 (2012) no. 3, pp. 1827-1917.

Voir la notice de l'article provenant de la source Annals of Mathematics website

For random collections of self-avoiding loops in two-dimensional domains, we define a simple and natural conformal restriction property that is conjecturally satisfied by the scaling limits of interfaces in models from statistical physics. This property is basically the combination of conformal invariance and the locality of the interaction in the model. Unlike the Markov property that Schramm used to characterize SLE curves (which involves conditioning on partially generated interfaces up to arbitrary stopping times), this property only involves conditioning on entire loops and thus appears at first glance to be weaker.
DOI : 10.4007/annals.2012.176.3.8

Scott Sheffield 1 ; Wendelin Werner 2

1 Department of Mathematics<br/> Massachusetts Institute of Technology<br/> 77 Massachusetts Ave.<br/> Cambridge, MA 02139
2 Laboratoire de Mathématiques<br/> Université Paris-Sud <br/> 91405 Orsay<br/> France<br/> and <br/> Ecole Normale Supérieure<br/> 75230 Paris<br/> France 
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Scott Sheffield; Wendelin Werner. Conformal loop ensembles: the Markovian characterization and the loop-soup construction. Annals of mathematics, Tome 176 (2012) no. 3, pp. 1827-1917. doi : 10.4007/annals.2012.176.3.8. http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.176.3.8/

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