Exit problems associated with affine reflection groups

Details Exit problems associated with affine reflection groups Exit problems associated with affine reflection groups

2007-07-13

arxiv.org/abs/0707.2009v2

Mathematics

Probability

34 pages. Rewritten in some places to improve presentation. To appear in Probability Theory and Related Fields

Scientific paper

10.1007/s00440-008-0171-9

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 \~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.

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