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Exit problems associated with finite reflection groups
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UNSPECIFIED (2005) Exit problems associated with finite reflection groups. PROBABILITY THEORY AND RELATED FIELDS, 132 (4). pp. 501-538. doi:10.1007/s00440-004-0402-7 ISSN 0178-8051.
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Official URL: http://dx.doi.org/10.1007/s00440-004-0402-7
Abstract
We obtain a formula for the distribution of the first exit time of Brownian motion from a fundamental region associated with a finite reflection group. In the type A case it is closely related to a formula of de Bruijn and the exit probability is expressed as a Pfaffian. Our formula yields a generalisation of de Bruijn's. We derive large and small time asymptotics, and formulas for expected first exit times. The results extend to other Markov processes. By considering discrete random walks in the type A case we recover known formulas for the number of standard Young tableaux with bounded height.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Journal or Publication Title: | PROBABILITY THEORY AND RELATED FIELDS | ||||
| Publisher: | SPRINGER | ||||
| ISSN: | 0178-8051 | ||||
| Official Date: | July 2005 | ||||
| Dates: |
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| Volume: | 132 | ||||
| Number: | 4 | ||||
| Number of Pages: | 38 | ||||
| Page Range: | pp. 501-538 | ||||
| DOI: | 10.1007/s00440-004-0402-7 | ||||
| Publication Status: | Published |
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