A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian
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...
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| Datum: | 2015 |
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| Sprache: | English |
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Інститут математики НАН України
2015
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/146999 |
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| Zitieren: | 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. |
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irk-123456789-1469992019-02-13T01:23:37Z A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian Rösler, M. Voit, M. 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. 2015 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Rösler, M. Voit, M. |
| spellingShingle |
Rösler, M. Voit, M. A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Rösler, M. Voit, M. |
| author_sort |
Rösler, M. |
| title |
A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian |
| title_short |
A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian |
| title_full |
A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian |
| title_fullStr |
A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian |
| title_full_unstemmed |
A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian |
| title_sort |
central limit theorem for random walks on the dual of a compact grassmannian |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146999 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2025-07-11T01:07:25Z |
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