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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2015 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2015
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146999 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862590329352355840 |
|---|---|
| author | Rösler, M. Voit, M. |
| author_facet | Rösler, M. Voit, M. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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| first_indexed | 2025-11-27T04:31:13Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146999 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-27T04:31:13Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Rösler, M. Voit, M. 2019-02-12T18:12:01Z 2019-02-12T18:12:01Z 2015 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 https://nasplib.isofts.kiev.ua/handle/123456789/146999 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian Article published earlier |
| spellingShingle | A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian Rösler, M. Voit, M. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146999 |
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