Exit problems associated with affine reflection groups

Doumerc, You and Moriarty, John (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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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 � 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 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User:	Ms Lucy van Russelt
Date Deposited:	18 Feb 2011
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1585

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