Matrix kernels for the Gaussian orthogonal and symplectic ensembles
Annales de l'Institut Fourier, Volume 55 (2005) no. 6, pp. 2197-2207.

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.

DOI: 10.5802/aif.2158
Classification: 60F99, 47B34
Keywords: random matrices, Gaussian orthogonal, symplectic ensembles
Mot clés : matrices aléatoires, ensemble Gaussien orthogonal, ensemble Gaussien symplectique, limite au bord du spectre

A. Tracy, Craig 1; Widom, Harold 

1 University of California, department of mathematics, Davis CA 95616 (USA), University of California, department of mathematics, Santa Cruz CA 95064 (USA)
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.2158/

[1] P.L. Ferrari 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] P.J. Forrester; T. Nagao; G. Honner 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] J. Baik; E.M. Rains; P.M. Bleher and A.R. Its Symmetrized random permutations, Random Matrix Models and Their Applications (2001), pp. 1-19 | Zbl

[4] I.C. Gohberg; M.G. Krein Introduction to the Theory of Linear Nonselfadjoint Operators, Transl. Math. Monogr., 35, Providence RI: Amer. Math. Soc., 1969 | MR | Zbl

[5] K. Johansson; III Toeplitz determinants, random growth and determinantal processes, Proc. of the International Congress of Mathematicians (2002), p. 53-52 | Zbl

[6] M.L. Mehta Random Matrices, London: Academic Press, 1991 | MR | Zbl

[7] F.W.J. Olver Asymptotics and Special Functions, New York: Academic Press, 1974 | MR | Zbl

[8] M. Prähofer; H. Spohn Universal distributions for growth processes in 1+1 dimensions and random matrices, Phys. Rev. Letts., Volume 84 (2000), pp. 4882-4885 | DOI

[9] C.A. Tracy; H. Widom On orthogonal and symplectic matrix ensembles, Commun. Math. Phys., Volume 177 (1996), pp. 727-754 | DOI | MR | Zbl

[10] C.A. Tracy; H. Widom Correlation functions, cluster functions and spacing distributions for random matrices, J. Stat. Phys., Volume 92 (1998), pp. 809-835 | DOI | MR | Zbl

[11] C.A. Tracy; H. Widom Distribution functions for largest eigenvalues and their applications (Proc. of the International Congress of Mathematicians), Volume I (2002), pp. 587-596 | Zbl

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