no. 6
Eigenvalues of Hermite and Laguerre ensembles : large beta asymptotics
Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 6, pp. 1083-1099. 
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     title = {Eigenvalues of {Hermite} and {Laguerre} ensembles : large beta asymptotics},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {1083--1099},
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Dumitriu, Ioana; Edelman, Alan. Eigenvalues of Hermite and Laguerre ensembles : large beta asymptotics. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 6, pp. 1083-1099. doi : 10.1016/j.anihpb.2004.11.002. http://www.numdam.org/articles/10.1016/j.anihpb.2004.11.002/

[1] Abramowitz M., Stegun I.A. (Eds.), Handbook of Mathematical Functions, Dover, New York, 1970.

[2] T. Baker, P. Forrester, The Calogero-Sutherland model and generalized classical polynomials, Commun. Math. Phys. 188 (1997) 175-216. | MR | Zbl

[3] J. Demmel, Applied Numerical Linear Algebra, SIAM, Philadelphia, PA, 1997. | MR | Zbl

[4] P. Diaconis, Patterns in eigenvalues: the 70th Josiah Willard Gibbs Lecture, Bull. Amer. Math. Soc. 40 (2003) 155-178. | MR | Zbl

[5] I. Dumitriu, A. Edelman, Matrix models for beta-ensembles, J. Math. Phys. 43 (2002) 5830-5847. | MR | Zbl

[6] I. Dumitriu, A. Edelman, G. Shuman, MOPS: Multivariate Orthogonal Polynomials (symbolically), 2004, Preprint found at, lanl.arxiv.org/abs/math-ph/0409066. | MR

[7] K. Johansson, On fluctuations of random hermitian matrices, Duke Math. J. 91 (1998) 151-203. | MR | Zbl

[8] K. Johansson, Shape fluctuations and random matrices, Commun. Math. Phys. 209 (2000) 437-476. | MR | Zbl

[9] I.M. Johnstone, On the distribution of the largest principal component, Ann. Statist. 29 (2) (2001) 295-327. | MR | Zbl

[10] M. Lal Mehta, Random Matrices, Academic Press, Boston, 1991. | MR | Zbl

[11] G. Szegö, Orthogonal Polynomials, American Mathematical Society, Providence, RI, 1975. | MR

[12] J.W. Silverstein, Z.D. Bai, CLT of linear spectral statistics of large dimensional sample covariance matrices, Preprint, 2003, Ann. Probab., accepted for publication. | MR | Zbl

[13] C.A. Tracy, H. Widom, On orthogonal and symplectic matrix ensembles, J. Statist. Phys. 92 (1996) 809-835. | MR

[14] C.A. Tracy, H. Widom, The distribution of the largest eigenvalue in the Gaussian ensembles, in: Calogero-Moser-Sutherland Models, CRM Ser. in Math. Phys., vol. 4, Springer-Verlag, 2000, pp. 461-472. | MR

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