[Représenta\-tions intégrales pour les polynômes d'Hermite et de Laguerre multiples]
On présente des représentations intégrales doubles pour les polynômes d'Hermite et de Laguerre multiples, aussi bien ceux de type I que ceux de type II. On montre aussi la connexion avec les représentations intégrales de certains noyaux de la théorie des matrices aléatoires.
We give integral representations for multiple Hermite and multiple Laguerre polynomials of both type I and II. We also show how these are connected with double integral representations of certain kernels from random matrix theory.
Keywords: Multiple orthogonal polynomials, random matrices, Christoffel-Darboux formula
Mot clés : polynômes orthogonaux multiples, matrices aléatoires, formule de Christoffel-Darboux
@article{AIF_2005__55_6_2001_0,
author = {M. BLEHER, Pavel and B.J. Kuijlaars, Arno},
title = {Integral representations for multiple {Hermite} and multiple {Laguerre} polynomials},
journal = {Annales de l'Institut Fourier},
pages = {2001--2014},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {55},
number = {6},
year = {2005},
doi = {10.5802/aif.2148},
mrnumber = {2187942},
zbl = {1084.33008},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2148/}
}
TY - JOUR AU - M. BLEHER, Pavel AU - B.J. Kuijlaars, Arno TI - Integral representations for multiple Hermite and multiple Laguerre polynomials JO - Annales de l'Institut Fourier PY - 2005 SP - 2001 EP - 2014 VL - 55 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2148/ DO - 10.5802/aif.2148 LA - en ID - AIF_2005__55_6_2001_0 ER -
%0 Journal Article %A M. BLEHER, Pavel %A B.J. Kuijlaars, Arno %T Integral representations for multiple Hermite and multiple Laguerre polynomials %J Annales de l'Institut Fourier %D 2005 %P 2001-2014 %V 55 %N 6 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2148/ %R 10.5802/aif.2148 %G en %F AIF_2005__55_6_2001_0
M. BLEHER, Pavel; B.J. Kuijlaars, Arno. Integral representations for multiple Hermite and multiple Laguerre polynomials. Annales de l'Institut Fourier, Tome 55 (2005) no. 6, pp. 2001-2014. doi : 10.5802/aif.2148. http://www.numdam.org/articles/10.5802/aif.2148/
[1] Multiple orthogonal polynomials, J. Comput. Appl. Math., Volume 99 (1998), pp. 423-447 | DOI | MR | Zbl
[2] Large limit of Gaussian random matrices with external source, part II (to appear in Comm. Math. Phys., preprint math-ph/0408041, http://arxiv.org/abs/math-ph/0408041)
[3] Multiple orthogonal polynomials for classical weights, Trans. Amer. Math. Soc., Volume 355 (2003), pp. 3887-3914 | DOI | MR | Zbl
[4] Phase transition of the largest eigenvalue for non-null complex sample covariance matrices (to appear in Ann. Prob., preprint math.PR/0403022, http://arxiv.org/abs/math.PR/0403022)
[5] Random matrices with external source and multiple orthogonal polynomials, Internat. Math. Research Notices (2004), pp. 109-129 | MR | Zbl
[6] Large limit of Gaussian random matrices with external source, part I, Commun. Math. Phys., Volume 252 (2004), pp. 43-76 | DOI | MR | Zbl
[7] Biorthogonal ensembles, Nuclear Phys., B, Volume 536 (1999), pp. 704-732 | MR | Zbl
[8] Correlations of nearby levels induced by a random potential, Nucl. Phys., B, Volume 479 (1996), pp. 697-706 | DOI | MR | Zbl
[9] Spectral form factor in a random matrix theory, Phys. Rev., Volume E 55 (1997), pp. 4067-4083 | MR
[10] Extension of level-spacing universality, Phys. Rev., Volume E 56 (1997), pp. 264-269
[11] Universal singularity at the closure of a gap in a random matrix theory, Phys. Rev., Volume E 57 (1998), pp. 4140-4149 | MR
[12] Level spacing of random matrices in an external source, Phys. Rev., Volume E 58 (1998), pp. 7176-7185 | MR
[13] A Christoffel-Darboux formula for multiple orthogonal polynomials, J. Approx. Theory, Volume 130 (2004), pp. 188-200 | MR | Zbl
[14] Differential operators on a semisimple Lie algebra, Amer. J. Math., Volume 79 (1957), pp. 87-120 | DOI | MR | Zbl
[15] Polynuclear growth model GOE and random matrix with deterministic source (preprint math-ph/0411057, http://arxiv.org/abs/math-ph/0411057)
[16] The planar approximation II, J. Math. Phys., Volume 21 (1980), pp. 411-421 | DOI | MR | Zbl
[17] Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices, Comm. Math. Phys., Volume 215 (2001) no. 3, pp. 683-705 | DOI | MR | Zbl
[18] Rational Approximation and Orthogonality, Translations of Mathematical Monographs, 92, Amer. Math. Soc., Providence R.I, 1991 | MR | Zbl
[19] The Pearcey process (preprint math.PR/0412005, http://arxiv.org/abs/math.PR/0412005) | Zbl
[20] Some classical multiple orthogonal polynomials, J. Comput. Appl. Math., Volume 127 (2001), pp. 317-347 | DOI | MR | Zbl
[21] Random Hermitian matrices in an external field, Nuclear Phys., Volume B 497 (1997), pp. 725-732 | MR | Zbl
[22] Universality of correlation functions of Hermitian random matrices in an external field, Comm. Math. Phys, Volume 194 (1998), pp. 631-650 | DOI | MR | Zbl
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