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Brownian beads
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  • Published: 14 October 2003

Brownian beads

  • Bálint Virág1 

Probability Theory and Related Fields volume 127, pages 367–387 (2003)Cite this article

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Abstract

We show that the past and future of half-plane Brownian motion at certain cutpoints are independent of each other after a conformal transformation. Like in Itô’s excursion theory, the pieces between cutpoints form a Poisson process with respect to a local time. The size of the path as a function of this local time is a stable subordinator whose index is given by the exponent of the probability that a stretch of the path has no cutpoint. The index is computed and equals 1/2.

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Authors and Affiliations

  1. Department of Mathematics, MIT, Cambridge, MA, 02139, USA

    Bálint Virág

Authors
  1. Bálint Virág
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Corresponding author

Correspondence to Bálint Virág.

Additional information

Research partially supported by NSF grant #DMS-0206781.

Mathematics Subject Classification (2000): 60J65; 30C35

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Cite this article

Virág, B. Brownian beads. Probab. Theory Relat. Fields 127, 367–387 (2003). https://doi.org/10.1007/s00440-003-0289-8

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  • Received: 12 May 2003

  • Revised: 07 June 2003

  • Published: 14 October 2003

  • Issue Date: November 2003

  • DOI: https://doi.org/10.1007/s00440-003-0289-8

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Keywords

  • Local Time
  • Poisson Process
  • Conformal Transformation
  • Stable Subordinator
  • Excursion Theory
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