We derive the limiting matrix kernels for the Gaussian orthogonal and symplectic ensembles scaled at the edge, with proofs of convergence in the operator norms that ensure convergence of the determinants.
Nous obtenons la limite au bord du spectre pour les noyaux matriciels des ensembles Gaussiens orthogonaux et symplectiques, avec preuves de convergence en norme d'opérateur qui garantissent la convergence des déterminants.
Keywords: random matrices, Gaussian orthogonal, symplectic ensembles
Mot clés : matrices aléatoires, ensemble Gaussien orthogonal, ensemble Gaussien symplectique, limite au bord du spectre
@article{AIF_2005__55_6_2197_0, author = {A. Tracy, Craig and Widom, Harold}, title = {Matrix kernels for the {Gaussian} orthogonal and symplectic ensembles}, journal = {Annales de l'Institut Fourier}, pages = {2197--2207}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {55}, number = {6}, year = {2005}, doi = {10.5802/aif.2158}, mrnumber = {2187952}, zbl = {1084.60022}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2158/} }
TY - JOUR AU - A. Tracy, Craig AU - Widom, Harold TI - Matrix kernels for the Gaussian orthogonal and symplectic ensembles JO - Annales de l'Institut Fourier PY - 2005 SP - 2197 EP - 2207 VL - 55 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2158/ DO - 10.5802/aif.2158 LA - en ID - AIF_2005__55_6_2197_0 ER -
%0 Journal Article %A A. Tracy, Craig %A Widom, Harold %T Matrix kernels for the Gaussian orthogonal and symplectic ensembles %J Annales de l'Institut Fourier %D 2005 %P 2197-2207 %V 55 %N 6 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2158/ %R 10.5802/aif.2158 %G en %F AIF_2005__55_6_2197_0
A. Tracy, Craig; Widom, Harold. Matrix kernels for the Gaussian orthogonal and symplectic ensembles. Annales de l'Institut Fourier, Volume 55 (2005) no. 6, pp. 2197-2207. doi : 10.5802/aif.2158. http://archive.numdam.org/articles/10.5802/aif.2158/
[1] Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues, Commun. Math. Phys., Volume 252 (2004), pp. 77-109 | DOI | MR | Zbl
[2] Correlations for the orthogonal-unitary and symplectic-unitary transitions at the soft and hard edges, Nucl. Phys., Volume B 553 (1999), pp. 601-643 | MR | Zbl
[3] Symmetrized random permutations, Random Matrix Models and Their Applications (2001), pp. 1-19 | Zbl
[4] Introduction to the Theory of Linear Nonselfadjoint Operators, Transl. Math. Monogr., 35, Providence RI: Amer. Math. Soc., 1969 | MR | Zbl
[5] Toeplitz determinants, random growth and determinantal processes, Proc. of the International Congress of Mathematicians (2002), p. 53-52 | Zbl
[6] Random Matrices, London: Academic Press, 1991 | MR | Zbl
[7] Asymptotics and Special Functions, New York: Academic Press, 1974 | MR | Zbl
[8] Universal distributions for growth processes in dimensions and random matrices, Phys. Rev. Letts., Volume 84 (2000), pp. 4882-4885 | DOI
[9] On orthogonal and symplectic matrix ensembles, Commun. Math. Phys., Volume 177 (1996), pp. 727-754 | DOI | MR | Zbl
[10] Correlation functions, cluster functions and spacing distributions for random matrices, J. Stat. Phys., Volume 92 (1998), pp. 809-835 | DOI | MR | Zbl
[11] Distribution functions for largest eigenvalues and their applications (Proc. of the International Congress of Mathematicians), Volume I (2002), pp. 587-596 | Zbl
Cited by Sources: