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Exit problems associated with finite reflection groups
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  • Published: 10 February 2005

Exit problems associated with finite reflection groups

  • Yan Doumerc1 &
  • Neil O’Connell2 

Probability Theory and Related Fields volume 132, pages 501–538 (2005)Cite this article

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Abstract.

We obtain a formula for the distribution of the first exit time of Brownian motion from a fundamental region associated with a finite reflection group. In the type A case it is closely related to a formula of de Bruijn and the exit probability is expressed as a Pfaffian. Our formula yields a generalisation of de Bruijn’s. We derive large and small time asymptotics, and formulas for expected first exit times. The results extend to other Markov processes. By considering discrete random walks in the type A case we recover known formulas for the number of standard Young tableaux with bounded height.

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Author information

Authors and Affiliations

  1. Institut de Mathématiques, Laboratoire de Statistique et Probabilités, Université Paul-Sabatier, Toulouse, France

    Yan Doumerc

  2. Mathematics Institute, University of Warwick, France

    Neil O’Connell

Authors
  1. Yan Doumerc
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  2. Neil O’Connell
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Mathematics Subject Classification (2000): 20F55, 60J65

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Cite this article

Doumerc, Y., O’Connell, N. Exit problems associated with finite reflection groups. Probab. Theory Relat. Fields 132, 501–538 (2005). https://doi.org/10.1007/s00440-004-0402-7

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  • Received: 28 May 2004

  • Revised: 24 October 2004

  • Published: 10 February 2005

  • Issue Date: July 2005

  • DOI: https://doi.org/10.1007/s00440-004-0402-7

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Keywords

  • Reflection
  • Stochastic Process
  • Brownian Motion
  • Probability Theory
  • Markov Process
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