Eigenvalues of Hermite and Laguerre ensembles : large beta asymptotics
Dumitriu, Ioana ; Edelman, Alan
Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005), p. 1083-1099 / Harvested from Numdam
@article{AIHPB_2005__41_6_1083_0,
     author = {Dumitriu, Ioana and Edelman, Alan},
     title = {Eigenvalues of Hermite and Laguerre ensembles : large beta asymptotics},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {41},
     year = {2005},
     pages = {1083-1099},
     doi = {10.1016/j.anihpb.2004.11.002},
     mrnumber = {2172210},
     zbl = {1079.15014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2005__41_6_1083_0}
}
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) pp. 1083-1099. doi : 10.1016/j.anihpb.2004.11.002. http://gdmltest.u-ga.fr/item/AIHPB_2005__41_6_1083_0/

[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 1471336 | Zbl 0903.33010

[3] J. Demmel, Applied Numerical Linear Algebra, SIAM, Philadelphia, PA, 1997. | MR 1463942 | Zbl 0879.65017

[4] P. Diaconis, Patterns in eigenvalues: the 70th Josiah Willard Gibbs Lecture, Bull. Amer. Math. Soc. 40 (2003) 155-178. | MR 1962294 | Zbl 01896626

[5] I. Dumitriu, A. Edelman, Matrix models for beta-ensembles, J. Math. Phys. 43 (2002) 5830-5847. | MR 1936554 | Zbl 1060.82020

[6] I. Dumitriu, A. Edelman, G. Shuman, MOPS: Multivariate Orthogonal Polynomials (symbolically), 2004, Preprint found at, lanl.arxiv.org/abs/math-ph/0409066. | MR 2325917

[7] K. Johansson, On fluctuations of random hermitian matrices, Duke Math. J. 91 (1998) 151-203. | MR 1487983 | Zbl 1039.82504

[8] K. Johansson, Shape fluctuations and random matrices, Commun. Math. Phys. 209 (2000) 437-476. | MR 1737991 | Zbl 0969.15008

[9] I.M. Johnstone, On the distribution of the largest principal component, Ann. Statist. 29 (2) (2001) 295-327. | MR 1863961 | Zbl 1016.62078

[10] M. Lal Mehta, Random Matrices, Academic Press, Boston, 1991. | MR 1083764 | Zbl 0780.60014

[11] G. Szegö, Orthogonal Polynomials, American Mathematical Society, Providence, RI, 1975. | MR 372517

[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 2040792 | Zbl 1063.60022

[13] C.A. Tracy, H. Widom, On orthogonal and symplectic matrix ensembles, J. Statist. Phys. 92 (1996) 809-835. | MR 1385083

[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 1844228