Probability Theory and Related Fields

, Volume 145, Issue 3–4, pp 351–383 | Cite as

Exit problems associated with affine reflection groups

  • Yan Doumerc
  • John MoriartyEmail author


We obtain a formula for the distribution of the first exit time of Brownian motion from the alcove of an affine Weyl group. In most cases the formula is expressed compactly, in terms of Pfaffians. Expected exit times are derived in the type \({\widetilde{A}}\) case. The results extend to other Markov processes. We also give formulas for the real eigenfunctions of the Dirichlet and Neumann Laplacians on alcoves, observing that the ‘Hot Spots’ conjecture of J. Rauch is true for alcoves.


Brownian Motion Weyl Group Equilateral Triangle Exit Time Consistent Subset 
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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Classes PréparatoireLycée Gaston BergerLille CedexFrance
  2. 2.School of MathematicsUniversity of ManchesterManchesterUK

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