Exit problems associated with affine reflection groups
Probability
2013-02-12 v2 Group Theory
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 \~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.
Keywords
Cite
@article{arxiv.0707.2009,
title = {Exit problems associated with affine reflection groups},
author = {Yan Doumerc and John Moriarty},
journal= {arXiv preprint arXiv:0707.2009},
year = {2013}
}
Comments
34 pages. Rewritten in some places to improve presentation. To appear in Probability Theory and Related Fields