A Christoffel-Darboux formula for multiple orthogonal polynomials

Preprint

3 February 2004

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0402031

Abstract

Bleher and Kuijlaars recently showed that the eigenvalue correlations from matrix ensembles with external source can be expressed by means of a kernel built out of special multiple orthogonal polynomials. We derive a Christoffel-Darboux formula for this kernel for general multiple orthogonal polynomials. In addition, we show that the formula can be written in terms of the solution of the Riemann-Hilbert problem for multiple orthogonal polynomials, which will be useful for asymptotic analysis.

Keywords

MULTIPLE ORTHOGONAL POLYNOMIALS
CHRISTOFFEL DARBOUX FORMULA
CORRELATIONS FROM MATRIX
ORTHOGONAL POLYNOMIALS
DARBOUX FORMULA
EIGENVALUE

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