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A Christoffel-Darboux formula for multiple orthogonal polynomials

E. Daems·A. B. J. Kuijlaars
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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.

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E. Daems, A. B. J. Kuijlaars. 2004-02-03. A Christoffel-Darboux formula for multiple orthogonal polynomials. https://arxiv.org/abs/math/0402031

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