Multivariable Christoffel-Darboux kernels and characteristic polynomials of random hermitian matrices

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2006
• Main Author: Rosengren, H.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2006
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146068
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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...