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 problčmes 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.