Riemann-Hilbert Problems for Multiple Orthogonal Polynomials

By Walter Van Assche, Jeffrey S. Geronimo, Arno B. J. Kuijlaars. 2001

142 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/a0d035a16dfcda9abb71701a6447ada17e918b53

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Alexander I. Aptekarev
2. Arno B. J. Kuijlaars
3. Pavel Bleher
4. Walter Van Assche
5. Maxim L. Yattselev
6. K. Mclaughlin
7. Andrei Martínez-Finkelshtein

In Applied Mathematics

1. Arno B. J. Kuijlaars
2. Alexander I. Aptekarev
3. Pavel Bleher
4. Walter Van Assche
5. M. Y. Mo
6. Andrei Martínez-Finkelshtein
7. K. Mclaughlin
8. Maxim L. Yattselev

Citations in the corpus

• Riemann-Hilbert Analysis for Orthogonal Polynomials (2003, background): “Later developments related to orthogonal polynomials include [2, 3, 5, 18, 20, 21, 22, 23, 34].”
• Orthogonal polynomials (2005, unknown): “There is an approach (see Van Assche–Geronimo–Kuijlaars [96]) to both types of multiple orthogonality in terms of matrix-valued Riemann–Hilbert problem for (r + 1)× (r + 1) matrices Y = (Yij(z))ri,j=0.”
• Multiple orthogonal polynomial ensembles (2009, methodology): “on kernel Kn given by the determinant (3.5) has another expression in terms of the RH problem for multiple orthogonal polynomials. MOPs (with pweights) satisfy a (p+ 1)×(p+1) matrix valued RH problem [68] • Y : C\R→ C (p+1)× is analytic, MULTIPLE ORTHOGONAL POLYNOMIAL ENSEMBLES 9 • Y+(x) = Y−(x) ”
• Large n Limit of Gaussian Random Matrices with External Source, Part I (2004, background): “These are characterized by a matrix RH problem [ 32 ], and the eigenvalue correlation kernel of (1.1) has a direct expression in terms of the solution of this RH problem, see [5, 14] and also formula (1.14) below.”
• Rank 1 real Wishart spiked model (2011, background): “Then the multi-orthognoal polynomials of type II P II N,l(x), [3], [4], [18], [40] are polynomials of degree N − 1 such that”
• Asymptotics of Hermite–Padé Rational Approximants for Two Analytic Functions with Separated Pairs of Branch Points (Case of Genus 0) (2007, methodology): “In [74] multiple orthogonality for Hermite-Padé polynomials was reformulated in terms of a (p+1)×(p+1) matrix-valued Riemann-Hilbert problem.”