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Probability Theory and Related Fields

, Volume 132, Issue 4, pp 501–538 | Cite as

Exit problems associated with finite reflection groups

  • Yan Doumerc
  • Neil O’Connell
Article

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.

Keywords

Reflection Stochastic Process Brownian Motion Probability Theory Markov Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Yan Doumerc
    • 1
  • Neil O’Connell
    • 2
  1. 1.Institut de Mathématiques, Laboratoire de Statistique et ProbabilitésUniversité Paul-SabatierToulouseFrance
  2. 2.Mathematics InstituteUniversity of WarwickFrance

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