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The Brownian loop soup
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  • Published: 02 January 2004

The Brownian loop soup

  • Gregory F. Lawler1 &
  • Wendelin Werner2 

Probability Theory and Related Fields volume 128, pages 565–588 (2004)Cite this article

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  • 131 Citations

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Abstract.

We define a natural conformally invariant measure on unrooted Brownian loops in the plane and study some of its properties. We relate this measure to a measure on loops rooted at a boundary point of a domain and show how this relation gives a way to ‘‘chronologically add Brownian loops’’ to simple curves in the plane.

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Author information

Authors and Affiliations

  1. Department of Mathematics, 310 Malott Hall, Cornell University, Ithaca, NY, 14853-4201, USA

    Gregory F. Lawler

  2. Laboratoire de Mathématiques, Bât. 425, Université Paris-Sud, 91405, Orsay cedex, France

    Wendelin Werner

Authors
  1. Gregory F. Lawler
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  2. Wendelin Werner
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Corresponding author

Correspondence to Wendelin Werner.

Additional information

Cornell University; Research supported in part by the National Science Foundation

Université Paris-Sud and IUF

Mathematics Subject Classification (2000): 60J65, 81T40

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Lawler, G., Werner, W. The Brownian loop soup. Probab. Theory Relat. Fields 128, 565–588 (2004). https://doi.org/10.1007/s00440-003-0319-6

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  • Received: 14 May 2003

  • Revised: 27 October 2003

  • Published: 02 January 2004

  • Issue Date: April 2004

  • DOI: https://doi.org/10.1007/s00440-003-0319-6

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Keywords

  •  Brownian loops
  • Conformal invariance
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