# Planar orthogonal polynomials as Type II multiple orthogonal polynomials

@article{Lee2018PlanarOP,
title={Planar orthogonal polynomials as Type II multiple orthogonal polynomials},
author={Seung-Yeop Lee and Meng Yang},
journal={Journal of Physics A: Mathematical and Theoretical},
year={2018},
volume={52}
}
• Published 3 January 2018
• Mathematics
• Journal of Physics A: Mathematical and Theoretical
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.
• Mathematics
• 2022
A recent result of S.-Y. Lee and M. Yang states that the planar orthogonal polynomials orthogonal with respect to a modiﬁed Gaussian measure are also multiple orthogonal polynomials of type II on a
• Mathematics
• 2022
Explicit expressions for the Hahn multiple polynomials of type I, in terms of Kampé de Fériet hypergeometric series, are given. Orthogonal and biorthogonal relations are proven. Then, part of the
• Mathematics
• 2022
We study the characteristic polynomial p n ( x ) = Q n j =1 ( | z j | − x ) where the z j are drawn from the Mittag-Leﬄer ensemble, i.e. a two-dimensional determinantal point process which
. We consider a two-dimensional equilibrium measure problem under the presence of quadratic potentials with a point charge and derive the explicit shape of the associated droplets. This particularly
• Mathematics
• 2022
. We consider determinantal Coulomb gas ensembles with a class of discrete rotational symmetric potentials whose droplets consist of several disconnected components. Under the insertion of a point
• Mathematics
• 2020
We study expectations of powers and correlation functions for characteristic polynomials of N×N non-Hermitian random matrices. For the 1-point and 2-point correlation function, we obtain several
• Mathematics
• 2021
We consider a family of random normal matrix models whose eigenvalues tend to occupy lemniscate type droplets as the size of the matrix increases. Under the insertion of a point charge, we derive the
• Mathematics
• 2022
We obtain large n asymptotics for the m -point moment generating function of the disk counting statistics of the Mittag-Leﬄer ensemble. We focus on the critical regime where all disk boundaries are
• Mathematics
• 2020
We consider the planar orthogonal polynomial $p_{n}(z)$ with respect to the measure supported on the whole complex plane $${\rm e}^{-N|z|^2} \prod_{j=1}^\nu |z-a_j|^{2c_j}\,{\rm d} A(z)$$ where \${\rm

## References

SHOWING 1-10 OF 16 REFERENCES

• Mathematics
• 2012
We consider the orthogonal polynomials { Pn(z) } with respect to the measure | z−a |2Nce−N| z |2dA(z) over the whole complex plane. We obtain the strong asymptotic of the orthogonal polynomials in
Multiple orthogonal polynomials are a generalization of orthogonal polynomials in which the orthogonality is distributed among a number of orthogonality weights. They appear in random matrix theory
• Mathematics
• 2001
In the early nineties, Fokas, Its and Kitaev observed that there is a natural Riemann-Hilbert problem (for 2 x×2 matrix functions) associated with a system of orthogonal polynomials. This
• Mathematics
Proceedings of the London Mathematical Society
• 2018
In this article, we study the large N asymptotics of complex moments of the absolute value of the characteristic polynomial of an N×N complex Ginibre random matrix with the characteristic polynomial
This paper considers the zero distribution of Hermite–Padé polynomials of the first kind associated with a vector function whose components are functions with a finite number of branch points in the
• Mathematics
• 2016
This is an extended version of our note in the Notices of the American Mathematical Society 63 (2016), no. 9, in which we explain what multiple orthogonal polynomials are and where they appear in
• Mathematics
• 2016
AbstractWe consider the orthogonal polynomials, $${\{P_n(z)\}_{n=0,1,\ldots}}$${Pn(z)}n=0,1,…, with respect to the measure $$|z-a|^{2c} e^{-N|z|^2}dA(z)$$|z-a|2ce-N|z|2dA(z)supported over the whole