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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| Дата: | 2006 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2006
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.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| id |
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irk-123456789-1460682019-02-07T01:23:56Z Multivariable Christoffel-Darboux kernels and characteristic polynomials of random hermitian matrices Rosengren, H. 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). 2006 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146068 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 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). |
| format |
Article |
| author |
Rosengren, H. |
| spellingShingle |
Rosengren, H. Multivariable Christoffel-Darboux kernels and characteristic polynomials of random hermitian matrices Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Rosengren, H. |
| author_sort |
Rosengren, H. |
| title |
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_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_sort |
multivariable christoffel-darboux kernels and characteristic polynomials of random hermitian matrices |
| publisher |
Інститут математики НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146068 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT rosengrenh multivariablechristoffeldarbouxkernelsandcharacteristicpolynomialsofrandomhermitianmatrices |
| first_indexed |
2023-05-20T17:23:44Z |
| last_indexed |
2023-05-20T17:23:44Z |
| _version_ |
1796153197470941184 |