Exit problems associated with affine reflection groups
成果类型：
Article
署名作者：
Doumerc, Yan; Moriarty, John
署名单位：
University of Manchester
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-008-0171-9
发表日期：
2009
页码：
351-383
关键词：
摘要：
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) over tilde 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.