Journal of the American Mathematical Society

Author(s): Wendelin Werner
Journal: J. Amer. Math. Soc. 21 (2008), 137-169.
MSC (2000): Primary 60D05; Secondary 82B41, 82B43, 30C99, 60J65
Posted: February 20, 2007
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Abstract: We show that there exists a unique (up to multiplication by constants) and natural measure on simple loops in the plane and on each Riemann surface, such that the measure is conformally invariant and also invariant under restriction (i.e. the measure on a Riemann surface

that is contained in another Riemann surface

is just the measure on

restricted to those loops that stay in

). We study some of its properties and consequences concerning outer boundaries of critical percolation clusters and Brownian loops.

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Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 60D05, 82B41, 82B43, 30C99, 60J65

Wendelin Werner
Affiliation: Université Paris-Sud, Laboratoire de Mathématiques, Université Paris-Sud, Bât. 425, 91405 Orsay cedex, France and DMA, Ecole Normale Supérieure, 45 rue d'Ulm, 75230 Paris cedex, France
Email: wendelin.werner@math.u-psud.fr

DOI: 10.1090/S0894-0347-07-00557-7
PII: S 0894-0347(07)00557-7
Received by editor(s): December 17, 2005
Posted: February 20, 2007
Additional Notes: This work was supported by the Institut Universitaire de France
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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ISSN: 1088-6834(e) ISSN: 0894-0347(p)

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