## 2011.17: Exit problems associated with affine reflection groups

2011.17:
You Doumerc and John Moriarty
(2009)
*Exit problems associated with affine reflection
groups.*
Probability Theory and Related Fields, 145 (3-4).
pp. 351-383.
ISSN 0178-8051

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DOI: 10.1007/s00440-008-0171-9

## Abstract

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 Ã case. The results extend to other Markov processes. We also give formulas for the real eigenfunctions of the Dirichlet and Neumann Laplacians on alcoves, and observe that the ‘Hot Spots’ conjecture of J. Rauch is true for alcoves.

Item Type: | Article |
---|---|

Subjects: | MSC 2000 > 60 Probability theory and stochastic processes |

MIMS number: | 2011.17 |

Deposited By: | Ms Lucy van Russelt |

Deposited On: | 18 February 2011 |

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