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The Riemann-Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1]

- A. Kuijlaars, K. Mclaughlin, W. Assche, M. Vanlessen
- Mathematics
- 23 November 2001

Singular Values of Products of Ginibre Random Matrices, Multiple Orthogonal Polynomials and Hard Edge Scaling Limits

- A. Kuijlaars, Lun Zhang
- Mathematics
- 5 August 2013

Akemann, Ipsen and Kieburg recently showed that the squared singular values of products of M rectangular random matrices with independent complex Gaussian entries are distributed according to a… Expand

Asymptotics for minimal discrete energy on the sphere

- A. Kuijlaars, E. Saff
- Mathematics
- 1995

We investigate the energy of arrangements of N points on the surface of the unit sphere Sd in Rd+1 that interact through a power law potential V = 1/rs, where s > 0 and r is Euclidean distance. With… Expand

The Asymptotic Zero Distribution of Orthogonal Polynomials with Varying Recurrence Coefficients

- A. Kuijlaars, W. Assche
- Mathematics
- 1 July 1999

We study the zeros of orthogonal polynomials pn, N, n=0, 1, ?, that are generated by recurrence coefficients an, N and bn, N depending on a parameter N. Assuming that the recurrence coefficients… Expand

Singular values of products of random matrices and polynomial ensembles

- A. Kuijlaars, Dries Stivigny
- Mathematics
- 23 April 2014

Akemann, Ipsen, and Kieburg showed recently that the squared singular values of a product of M complex Ginibre matrices are distributed according to a determinantal point process. We introduce the… Expand

Random matrices with external source and multiple orthogonal polynomials

- P. Bleher, A. Kuijlaars
- Mathematics
- 28 July 2003

We show that the average characteristic polynomial Pn(z) = E[det(zI−M)] of the random Hermitian matrix ensemble Z 1 n exp(−Tr(V (M) − AM))dM is characterized by multiple orthogonality conditions that… Expand

Large n Limit of Gaussian Random Matrices with External Source, Part I

- P. Bleher, A. Kuijlaars
- Mathematics
- 16 February 2004

AbstractWe consider the random matrix ensemble with an external source
defined on n×n Hermitian matrices, where A is a diagonal matrix with only two eigenvalues ±a of equal multiplicity. For the… Expand

Impossibility of Fast Stable Approximation of Analytic Functions from Equispaced Samples

- R. Platte, L. Trefethen, A. Kuijlaars
- MathematicsSIAM Rev.
- 1 May 2011

TLDR

Singular Value Statistics of Matrix Products with Truncated Unitary Matrices

- M. Kieburg, A. Kuijlaars, Dries Stivigny
- Mathematics
- 16 January 2015

We prove that the squared singular values of a fixed matrix multiplied with a truncation of a Haar distributed unitary matrix are distributed by a polynomial ensemble. This result is applied to a… Expand

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