Multivariable Christoffel-Darboux kernels and characteristic polynomials of random hermitian matrices
We study multivariable Christoffel-Darboux kernels, which may be viewed as reproducing kernels for antisymmetric orthogonal polynomials, and also as correlation functions for products of characteristic polynomials of random Hermitian matrices. Using their interpretation as reproducing kernels, we ob...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2006 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2006
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146068 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Multivariable Christoffel-Darboux kernels and characteristic polynomials of random hermitian matrices / H. Rosengren // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 32 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862532413225172992 |
|---|---|
| author | Rosengren, H. |
| author_facet | Rosengren, H. |
| citation_txt | Multivariable Christoffel-Darboux kernels and characteristic polynomials of random hermitian matrices / H. Rosengren // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 32 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study multivariable Christoffel-Darboux kernels, which may be viewed as reproducing kernels for antisymmetric orthogonal polynomials, and also as correlation functions for products of characteristic polynomials of random Hermitian matrices. Using their interpretation as reproducing kernels, we obtain simple proofs of Pfaffian and determinant formulas, as well as Schur polynomial expansions, for such kernels. In subsequent work, these results are applied in combinatorics (enumeration of marked shifted tableaux) and number theory (representation of integers as sums of squares).
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| first_indexed | 2025-11-24T04:38:01Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146068 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T04:38:01Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Rosengren, H. 2019-02-06T17:23:16Z 2019-02-06T17:23:16Z 2006 Multivariable Christoffel-Darboux kernels and characteristic polynomials of random hermitian matrices / H. Rosengren // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 32 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 15A15; 15A52; 42C05 https://nasplib.isofts.kiev.ua/handle/123456789/146068 We study multivariable Christoffel-Darboux kernels, which may be viewed as reproducing kernels for antisymmetric orthogonal polynomials, and also as correlation functions for products of characteristic polynomials of random Hermitian matrices. Using their interpretation as reproducing kernels, we obtain simple proofs of Pfaffian and determinant formulas, as well as Schur polynomial expansions, for such kernels. In subsequent work, these results are applied in combinatorics (enumeration of marked shifted tableaux) and number theory (representation of integers as sums of squares). This paper is a contribution to the Vadim Kuznetsov Memorial Issue “Integrable Systems and Related Topics”. I thank Alain Lascoux and Eric Rains for communicating their unpublished works, as well as for several useful comments. The research was supported by the Swedish Science Research Council (Vetenskapsradet). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Multivariable Christoffel-Darboux kernels and characteristic polynomials of random hermitian matrices Article published earlier |
| spellingShingle | Multivariable Christoffel-Darboux kernels and characteristic polynomials of random hermitian matrices Rosengren, H. |
| title | Multivariable Christoffel-Darboux kernels and characteristic polynomials of random hermitian matrices |
| title_full | Multivariable Christoffel-Darboux kernels and characteristic polynomials of random hermitian matrices |
| title_fullStr | Multivariable Christoffel-Darboux kernels and characteristic polynomials of random hermitian matrices |
| title_full_unstemmed | Multivariable Christoffel-Darboux kernels and characteristic polynomials of random hermitian matrices |
| title_short | Multivariable Christoffel-Darboux kernels and characteristic polynomials of random hermitian matrices |
| title_sort | multivariable christoffel-darboux kernels and characteristic polynomials of random hermitian matrices |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146068 |
| work_keys_str_mv | AT rosengrenh multivariablechristoffeldarbouxkernelsandcharacteristicpolynomialsofrandomhermitianmatrices |