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Multivariable Christoffel-Darboux kernels and characteristic polynomials of random hermitian matrices
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2006, том 2
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Multivariable Christoffel-Darboux kernels and characteristic polynomials of random hermitian matrices
Інший ID:
2000 Mathematics Subject Classification: 15A15; 15A52; 42C05
Посилання:
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.
Підтримка:
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 I thank Alain Lascoux and Eric Rains for communicating their unpublished works, as well as for several useful comments.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).
Дата:
2006
Переглядів:
612
Завантажень:
249
Анотація:
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).
