Arno Kuijlaars

Address:

Department of Mathematics
Katholieke Universiteit Leuven
Celestijnenlaan 200 B
B-3001 Leuven (Heverlee)
BELGIUM
tel: +32-16-32 70 52
fax: +32-16-32 79 98
Email: arno.kuijlaars@wis.kuleuven.be

I am professor at the Department of Mathematics. My research interests are in

Riemann-Hilbert problems and asymptotic analysis: steepest descent method for RH problems
Random matrix theory and determinantal point processes: large n limits and universality questions
Orthogonal polynomials and special functions, including Painlevé equations
Multiple orthogonal polynomials and vector equilibrium problems
Approximation theory

I teach the courses

Wiskunde 1, Wiskunde 2 (Bachelor Biochemie & Biotechnologie, Chemie, Geografie, Geologie, Informatica)
Bewijzen en Redeneren (Bachelor Fysica, Wiskunde)
Complexe Analyse (Bachelor Wiskunde)
Asymptotics and Special Functions (Master Wiskunde)

I am a member of the editorial board of the journals

Upcoming events

Numerical solution of the Painlevé equations, ICMS, Edinburgh, Scotland, May 10-14, 2010.
Conference on Random Matrices, Paris, France, June 1-4, 2010.
Orthogonal Polynomials in Probability Theory, Texas A&M University, U.S.A., July 6-10, 2010.
Orthogonal Polynomials, applications in Statistics and Stochastic Processes, Warwick, U.K., July 12-15, 2010.
International Congress of Mathematicians ICM2010, Hyderabad, India, August 19-27, 2010 (I am invited speaker at ICM2010 !).
Random Matrix Theory, Interacting Particle Systems and Integrable Systems, MSRI Berkeley, USA., August 16-December 17, 2010.
New Perspectives in Univariate and Multivariate Orthogonal Polynomials, Banff, Canada, October 10-15, 2010.
Foundations of Computational Mathematics (FOCM’11), Budapest, Hungary, July 4-14, 2011.

List of publications

New papers

(with P. Bleher and S. Delvaux) Random matrix model with external source and a vector equilibrium problem, manuscript (arXiv:1001.1238)
(with A. Deano and D. Huybrechs) Asymptotic zero distribution of complex orthogonal polynomials associated with Gaussian quadrature, manuscript (arXiv:1001.2219)
(with P. Román) Recurrence relations and vector equilibrium problems arising from a model of non-intersecting squared Bessel paths, manuscript (arXiv:0911.3831)
(with R.B. Platte and L.N. Trefethen) Impossibility of approximating analytic functions from equispaced samples, manuscript (E-prints archive)
(with M.Y. Mo) The global parametrix in the Riemann-Hilbert steepest descent analysis for orthogonal polynomials, manuscript (arXiv: 0909.5626)
(with S. Delvaux) A graph-based equilibrium problem for the limiting distribution of non-intersecting Brownian motions at low temperature, to appear in Constructive Approximation (arXiv:0907.2310)
Multiple orthogonal polynomial ensembles, in “Recent Trends in Orthogonal Polynomials and Approximation Theory” (J. Arvesú, F. Marcellán and A. Martínez-Finkelshtein eds.), Contemporary Mathematics 507, 2010. (arXiv:0902.1058)

Published papers 2005--

(with P.M.J. Tibboel) The asymptotic behaviour of recurrence coefficients for orthogonal polynomials with varying exponential weights, J. Comput. Math. Appl. 233 (2009), 775--785. (arXiv: 0708.3956)
(with S. Delvaux) A phase transition for non-intersecting Brownian motions and the Painlevé II equation, International Mathematics Research Notices 2009 (2009), 3639--3725. (arXiv:0809.1000)
(with A.R. Its and J. Östensson), Asymptotics for a special solution of the thirty fourth Painlevé equation, Nonlinearity 22 (2009), 1523--1558. (arXiv:0811.3847)
(with M. Duits) Universality in the two matrix model: a Riemann-Hilbert steepest descent analysis, Comm. Pure Appl. Math. 62 (2009), 1076--1153. (arXiv:0807.4814)
(with A. Martínez-Finkelshtein and F. Wielonsky) Non-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weights, Comm. Math. Phys. 286 (2009), 217--275. (arXiv:0712.1333)
(with D. Dai), Painlevé IV asymptotics for orthogonal polynomials with respect to a modified Laguerre weight, Studies in Applied Mathematics 122 (2009), 29--83. (arXiv:0804.2564)
(with E. Daems and W. Veys) Asymptotics of non-intersecting Brownian motions and a 4 x 4 Riemann-Hilbert problem, J. Approx. Theory 153 (2008), 225--256. (mathCV/0701923)
(with T. Claeys and M. Vanlessen) Multi-critical unitary random matrix ensembles and the general Painlevé II equation, Annals of Mathematics 168 (2008), 601--642. (math-ph/0508062)
(with T. Kriecherbauer, K.D.T-R McLaughlin, and P.D. Miller) Locating the zeros of partial sums of exp(z) with Riemann-Hilbert methods, in "Integrable Systems and Random Matrices: in honor of Percy Deift", Contemporary Mathematics 458, Amer. Math. Soc., Providence R.I. 2008, pp. 183--196. (arXiv:0709.1213)
(with T. Claeys) Universality in unitary random matrix ensembles when the soft edge meets the hard edge, in "Integrable Systems and Random Matrices: in honor of Percy Deift", Contemporary Mathematics 458, Amer. Math. Soc., Providence R.I. 2008, pp. 265--280. (math-ph/0701003)
(with A.R. Its and J. Östensson) Critical edge behavior in unitary random matrix ensembles and the thirty fourth Painlevé transcendent, Internat. Math. Research Notices 2008 (2008), article ID rnn017, 67 pages. (arXiv:0704.1972)
(with M. Duits) An equilibrium problem for the limiting eigenvalue distribution of banded Toeplitz matrices, SIAM J. Matrix Anal. Appl. 30 (2008), 173--196. (arXiv:0704.0378)
(with A.I. Aptekarev and W. Van Assche), Asymptotics of Hermite-Padé rational approximants for two analytic functions with separated pairs of branch points (case of genus 0), Internat. Math. Research Papers 2008 (2008), article ID rpm007, 128 pages. (arXiv:0708.0946)
(with H. Stahl, W. Van Assche and F. Wielonsky) Type II Hermite-Padé approximation to the exponential function, J. Comput. Appl. Math. 207 (2007), 227-244. (math.CA/0510278)
(with E. Daems) Multiple orthogonal polynomials of mixed type and non-intersecting Brownian motions, J. Approx. Theory 146 (2007), 91-114. (math.CA/0511470)
(with P.M. Bleher) Large n limit of Gaussian random matrices with external source, part III: double scaling limit, Comm. Math. Phys. 270 (2007), 481-517. (math.ph/0602064)
(with E.B. Saff and X. Sun) On separation of minimal Riesz energy points on spheres in Euclidean spaces, J. Comput. Appl. Math.199 (2007), 172-180. (math-ph/0503063)
(with M. Duits) Painlevé I asymptotics for orthogonal polynomials with respect to a varying quadratic weight, Nonlinearity 19 (2006), 2211-2245. (math.CA/0605201)
(with T. Claeys) Universality of the double scaling limit in random matrix models, Comm. Pure Appl. Math. 59 (2006), 1573-1603. (math-ph/0501074)
Convergence analysis of Krylov subspace iterations with methods from potential theory, SIAM Review 48 (2006), 3-40. (pdf-file)
(with P.M. Bleher) Integral representations for multiple Hermite and multiple Laguerre polynomials, Annales de l'Institut Fourier 55 (2005), 2001-2014. (math.CA/0406616)
(with A.I. Aptekarev and P.M. Bleher) Large n limit of Gaussian random matrices with external source, part II, Comm. Math. Phys. 259 (2005), 367-389. (math-ph/0408041)
(with S. Helsen and M. Van Barel) Convergence of the isometric Arnoldi process, SIAM J. Matrix Anal.Appl. 26 (2005), 782-809. (TW report 373)
(with A. Martínez-Finkelshtein and R. Orive) Orthogonality of Jacobi polynomials with general parameters, Electronic Transactions on Numerical Analysis 19 (2005), 1-17. (math.CA/0301037)
(with K. T-R McLaughlin) A Riemann-Hilbert problem for biorthogonal polynomials, J. Comput. Appl. Math. 178 (2005), 313-320. (math.CV/0310204)
(with W. Van Assche and F. Wielonsky) Quadratic Hermite-Padé approximation to the exponential function: a Riemann-Hilbert approach, Constr. Approx. 21 (2005), 351-412. (math.CA/0302357)

Published papers 2000--2004

(with A. Martínez-Finkelshtein) Strong asymptotics for Jacobi polynomials with varying nonstandard parameters, J. Anal. Math. 94 (2004), 195-234. (math.CA/0309443)
(with P.M. Bleher) Large n limit of Gaussian random matrices with external source, part I, Comm. Math. Phys. 252 (2004), 43-76. (math-ph/0402042)
(with E. Daems) A Christoffel-Darboux formula for multiple orthogonal polynomials, J. Approx. Theory 130 (2004), 188-200. (math.CA/0402031)
(with E.B. Davies) Spectral asymptotics of the non-self-adjoint harmonic oscillator, J. London Math. Soc. 70 (2004), 420-426.
(with K. T-R McLaughlin, W. Van Assche, and M. Vanlessen) The Riemann-Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1], Advances in Math. 188 (2004), 337-398. (math.CA/0111252)
(with K. T-R McLaughlin) Asymptotic zero behavior of Laguerre polynomial with negative parameter, Constr. Approx. 20 (2004), 497-523. (math.CA/0205175)
(with P.M. Bleher) Random matrices with external source and multiple orthogonal polynomials, Internat. Math. Research Notices 2004:3 (2004), 109-129. (math-ph/0307055)
(with M. Vanlessen), Universality for eigenvalue correlations at the origin of the spectrum, Comm. Math. Phys. 243 (2003), 163-191. (math-ph/0305044)
Riemann-Hilbert analysis for orthogonal polynomials, in: Orthogonal Polynomials and Special Functions (E. Koelink en W. Van Assche eds), Lecture Notes in Mathematics Vol. 1817, Springer-Verlag, 2003, pp. 167-210. (pdf-file)
(with H. Stahl, W. Van Assche, and F. Wielonsky) Asymptotique des approximants de Hermite-Padé quadratiques de la fonction exponentielle et problèmes de Riemann-Hilbert, Comptes Rendus Mathematique. Academie des Sciences. Paris 336 (2003), 893-896. (pdf-file)
(with B. Beckermann) Superlinear CG convergence for special right-hand sides, Elec. Trans. Numer. Anal. 14, (2002) 1-19.(ps-file) (pdf-file)
(with M. Vanlessen) Universality for eigenvalue correlations from the modified Jacobi unitary ensemble, Internat. Math. Research Notices 2002 No 30 (2002), 1575-1600. (math-ph/0204006)
(with J. Coussement and W. Van Assche) Direct and inverse spectral transform for the relativistic Toda lattice and the connection with Laurent orthogonality polynomials, Inverse Problems 18 (2002), 923-942. (math.CA/0204155)
(with K. T-R McLaughlin) Riemann--Hilbert analysis for Laguerre polynomials with large negative parameter, Comput. Methods Function Theory 1 (2001) 205-233. (math.CA/0204248)
(with S. Serra Capizzano) Asymptotic zero distribution of orthogonal polynomials with discontinuously varying recurrence coefficients, J. Approx. Theory 113 (2001), 142-155. (pdf-file)
(with B. Beckermann) On the sharpness of an asymptotic error estimate for Conjugate Gradients, BIT 41 (2001) 856-867. (pdf-file)
(with W. Van Assche and J.S. Geronimo) Riemann--Hilbert problems for multiple orthogonal polynomials, pp. 23-59 in: "NATO ASI Special Functions 2000. Current Perspective and Future Directions", (J. Bustoz, M.E.H. Ismail, S.K. Suslov eds.), Nato Science Series II Vol.30, Kluwer Academic Publishers, Dordrecht, 2001. (pdf-file)
(with K. T-R McLaughlin) Long time behavior of the continuum limit of the Toda lattice, and the generation of infinitely many gaps from $C^{\infty}$ initial data, Comm. Math. Phys. 221 (2001), 305-333. (pdf-file)
Asymptotic analysis of the density of states in random matrix models associated with a slowly decaying weight, J. Comput. Appl. Math. 133 (2001), 127-140. (pdf-file)
(with S.B. Damelin and P.D. Dragnev) The support of the equilibrium measure for a class of external fields on a finite interval, Pacific J. Math.199 (2001), 303-320. (pdf-file)
(with B. Beckermann) Superlinear convergence of Conjugate Gradients, SIAM J. Numer. Anal. 39 (2001), 300-329.(pdf-file)
On the finite gap ansatz in the continuum limit of the Toda lattice, Duke Math. J. 104 (2000), 433-462. (pdf-file)
Contracted zero distributions of extremal polynomials associated with slowly decaying weights, Constr. Approx. 16 (2000), 559-589. (pdf-file)
Which eigenvalues are found by the Lanczos method?, SIAM J. Matrix Anal. Appl. 22 (2000), 306-321. (pdf-file)
(with K. T-R McLaughlin) Generic behavior of the density of states in random matrix theory and equilibrium problems in the presence of real analytic external fields, Commun. Pure Appl. Math.53 (2000), 736-785. (pdf-file)

Published papers 1993--1999

(with S.B. Damelin) The support of the equilibrium measure in the presence of a monomial external field on [-1,1], Trans. Amer. Math. Soc. 351 (1999), 4561-4584.
(with W. Van Assche) The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients, J. Approx. Theory 99 (1999), 167-197.
(with W. Van Assche) Extremal polynomials on discrete sets, Proc. London Math. Soc. 79 (1999), 191-221.
(with P.D. Dragnev) Equilibrium problems associated with fast decreasing polynomials, Proc. Amer. Math. Soc. 127 (1999), 1065-1074.
Extremal problems for logarithmic potentials, in Approximation Theory IX, Volume I: Theoretical Aspects, (C.K. Chui and L.L. Schumaker, eds), Vanderbilt University Press, Nashville, TN, 1998, pp. 201-221.
(with E.A. Rakhmanov) Zero distributions for discrete orthogonal polynomials, J. Comput. Appl. Math. 99 (1998), 255-274. Corrigendum: J. Comput. Appl. Math.104 (1999), 213-213.
Best constants in one-sided weak-type inequalities, Methods. Appl. Analysis 5 (1998), 95-108.
(with W. Van Assche) A contact problem in elasticity related to weighted polynomials on the real line, Rendiconti del Circolo Matematico di Palermo, Suppl. 52 (1998), 575-587.
(with E.B. Saff) Asymptotics for minimal discrete energy on the sphere, Trans. Amer. Math. Soc. 350 (1998), 523-538.
(with W. Van Assche) A problem of Totik on fast decreasing polynomials, Constr. Approx. 14 (1998), 97-112.
(with W. Gautschi) Zeros and critical points of Sobolev orthogonal polynomials, J. Approx. Theory 91 (1997), 117-137.
(with E.B. Saff) Distributing many points on a sphere, Math. Intell. 19 (1997), 5-11.
Weighted approximation with varying weights: the case of a power-type singularity, J. Math. Anal. Appl. 204 (1996), 409-418.
A note on weighted polynomial approximation with varying weights, J. Approx. Theory 87 (1996), 112-115.
The role of the endpoint in weighted polynomial approximation with varying weights, Constr. Approx. 12 (1996), 287-301.
The zeros of Faber polynomials generated by an m-star, Math. Comp. 65 (1996), 151-156.
Chebyshev quadrature for measures with a strong singularity, J. Comput. Appl. Math. 65 (1995), 207-214.
Chebyshev-type quadrature for analytic weights on the circle and the interval, Indag. Math. N.S. 6 (1995), 419-432.
Chebyshev-type quadrature and zeros of Faber polynomials, J. Comput. Appl. Math. 62 (1995), 155-179.
(with E.B. Saff) Asymptotic distribution of the zeros of Faber polynomials, Math. Proc. Camb. Phil. Soc. 118 (1995), 437-447.
Chebyshev-type quadrature for Jacobi weight functions, J. Comput. Appl. Math. 57 (1995), 171-180.
Chebyshev-type quadrature and partial sums of the exponential series, Math. Comp. 64 (1995), 251-263.
(with J.G. Clunie) Approximation by polynomials with restricted zeros, J. Approx. Theory 79 (1994), 109-124.
(with T.L. McCoy) Answer to a query concerning the mapping $w = z^{1/m}$, Indag. Math. NS 4 (1993), 479-481.
The minimal number of nodes in Chebyshev type quadrature formulas, Indag. Math. NS 4 (1993), 339-362.