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Sur la forme des composantes connexes du complémentaire de la courbe brownienne plane
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  • Published: September 1994

Sur la forme des composantes connexes du complémentaire de la courbe brownienne plane

  • Wendelin Werner1 

Probability Theory and Related Fields volume 98, pages 307–337 (1994)Cite this article

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Résumé

Nous nous proposons d'étudier la forme des petites composantes connexes du complémentaire de la trajectoire brownienne plane. Nous montrons l'existence d'une loi limite de cette forme. De plus, nous obtenons un théorème limite qui montre que la donnée de l'ensemble des composantes connexes correspondant à une seule trajectoire suffit pour décrire cette loi.

Summary

We study the shape of the small connected components of the complement of a 2-dimensional Brownian path. We show the existence of an asymptotic law for this shape. Moreover, we prove a limit theorem that shows that the family of all the connected components of the complement of a single path contains all the information about this law.

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Références

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Authors and Affiliations

  1. Laboratoire de Probabilités, C.N.R.S., Université Pierre-et-Marie Curie, 4, place Jussieu, 75252, Paris Cedex 05, France

    Wendelin Werner

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  1. Wendelin Werner
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Cite this article

Werner, W. Sur la forme des composantes connexes du complémentaire de la courbe brownienne plane. Probab. Th. Rel. Fields 98, 307–337 (1994). https://doi.org/10.1007/BF01192257

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  • Received: 31 May 1993

  • Issue Date: September 1994

  • DOI: https://doi.org/10.1007/BF01192257

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Mathematics Subject Classification

  • 60J65
  • 60B05
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