Planar Orthogonal Polynomials As Type II Multiple Orthogonal Polynomials

Abstract

We show that the planar orthogonal polynomials with $l$ logarithmic singularities in the potential are the multiple orthogonal polynomials (Hermite-Padé polynomials) of Type II with $l$ measures. We also find the ratio between the determinant of the moment matrix corresponding to the multiple orthogonal polynomials and the determinant of the moment matrix from the original planar measure.

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Cited by in corpus (4)

• Characteristic polynomials of complex random matrices and Painlevé transcendents
• Strong Asymptotics of Planar Orthogonal Polynomials: Gaussian Weight Perturbed by Finite Number of Point Charges
• Exponential moments for disk counting statistics of random normal matrices in the critical regime
• Orthogonal polynomials in the normal matrix model with two insertions