A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian
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| Creator |
Rösler, M.
Voit, M. |
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| Description |
We consider compact Grassmann manifolds G/K over the real, complex or quaternionic numbers whose spherical functions are Heckman-Opdam polynomials of type BC. From an explicit integral representation of these polynomials we deduce a sharp Mehler-Heine formula, that is an approximation of the Heckman-Opdam polynomials in terms of Bessel functions, with a precise estimate on the error term. This result is used to derive a central limit theorem for random walks on the semi-lattice parametrizing the dual of G/K, which are constructed by successive decompositions of tensor powers of spherical representations of G. The limit is the distribution of a Laguerre ensemble in random matrix theory. Most results of this paper are established for a larger continuous set of multiplicity parameters beyond the group cases.
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| Date |
2019-02-12T18:12:01Z
2019-02-12T18:12:01Z 2015 |
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| Type |
Article
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| Identifier |
A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian / M. Rösler, M. Voit // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 32 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 33C52; 43A90; 60F05; 60B15; 43A62; 33C80; 33C67 DOI:10.3842/SIGMA.2015.013 http://dspace.nbuv.gov.ua/handle/123456789/146999 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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