Large deviations upper bounds and central limit theorems for non-commutative functionals of gaussian large random matrices
Guionnet, Alice
Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002), p. 341-384 / Harvested from Numdam
@article{AIHPB_2002__38_3_341_0,
     author = {Guionnet, Alice},
     title = {Large deviations upper bounds and central limit theorems for non-commutative functionals of gaussian large random matrices},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {38},
     year = {2002},
     pages = {341-384},
     mrnumber = {1899457},
     zbl = {0995.60028},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2002__38_3_341_0}
}
Guionnet, Alice. Large deviations upper bounds and central limit theorems for non-commutative functionals of gaussian large random matrices. Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) pp. 341-384. http://gdmltest.u-ga.fr/item/AIHPB_2002__38_3_341_0/

[1] L. Arnold, On the asymptotic distribution of eigenvalues of random matrices, J. Math. Anal. Appl. 20 (1967) 262-268. | MR 217833 | Zbl 0246.60029

[2] Z.D. Bai, Methodologies in spectral analysis of large dimensional random matrices: a review, Statistica Sinica 9 (1999) 611-661. | MR 1711663 | Zbl 0949.60077

[3] G. Ben Arous, A. Guionnet, Large deviations for Wigner's law and Voiculescu's non-commutative entropy, Probab. Theory Related Fields 108 (4) (1997) 517-542. | MR 1465640 | Zbl 0954.60029

[4] G. Ben Arous, O. Zeitouni, Large deviations from the circular law, ESAIM Probab. Statist. 2 (1998) 123-134. | Numdam | MR 1660943 | Zbl 0916.60022

[5] F.A. Berezin, Some remarks on the Wigner distribution, Teor. Mat. Fiz. 17 (1973) 1163-1171. | MR 465007 | Zbl 0291.60017

[6] P. Biane, Free brownian motion, free stochastic calculus and random matrices, in: Voiculescu D. (Ed.), Free Probability Theory, Fields Institute Communication, 12, American Math. Soc. , 1997, pp. 1-19. | MR 1426833 | Zbl 0873.60056

[7] P. Biane, Calcul stochastique non-commutatif, in: Saint Flour 1993, Lect. Notes in Math., 1608, Springer, Berlin, 1995, pp. 1-96. | MR 1383121 | Zbl 0878.60041

[8] A. Boutet De Monvel, A.M. Khorunzhy, Limit theorems for random matrices, Markov Proc. Related Fields 4 (1998) 175-197. | MR 1641617 | Zbl 0917.60040

[9] T. Cabanal-Duvillard, Fluctuations de la loi spectrale des grandes matrices aléatoires, Ann. Inst. H. Poincaré (2000), to appear.

[10] T. Cabanal-Duvillard, A. Guionnet, Large deviations upper bounds and non commutative entropies for some matrices ensembles, Annals of Probab. (2001), to appear. | MR 1872742

[11] G. Casati, V. Girko, Wigner's semicircle law for band matrices, Random Operators Stochastic Equations 1 (1993) 279-286. | MR 1254409 | Zbl 0839.60035

[12] A. Dembo, O. Zeitouni, Large Deviations Techniques and Applications, Jones and Bartlett Publishers, 1993. | MR 1202429 | Zbl 0793.60030

[13] F. Hiai, D. Petz, Eigenvalues density of the Wishart matrix and large deviations, Infinite Dimensional Anal. Quantum Prob. 1 (1998) 633-646. | MR 1665279 | Zbl 0934.60006

[14] A. Guionnet, O. Zeitouni, Concentration of the spectral measure for large matrices, Elec. Comm. Prob. 5 (2000) 14. | MR 1781846 | Zbl 0969.15010

[15] A. Guionnet, O. Zeitouni, Large deviations asymptotics for spherical integrals, J. Funct. Anal., in press. | MR 1883414 | Zbl 1002.60021

[16] A.M. Khorunzhy, B.A. Khoruzhenko, L.A. Pastur, Asymptotic properties of large random matrices with independent entries, J. Math. Phys. 37 (1996) 5033-5060. | MR 1411619 | Zbl 0866.15014

[17] A.M. Khorunzhy, B.A. Khoruzhenko, L.A. Pastur, M.V. Shcherbina, The large n-limit in statistical mechanics and the spectral theory of disordered systems phase, Transition and Critical Phenomena 15 (1992) 73-239.

[18] K. Johansson, On fluctuations of eigenvalues of random Hermitian matrices, Duke Math. J. 91 (1998) 151-204. | MR 1487983 | Zbl 1039.82504

[19] C. Kipnis, S. Olla, S.R.S. Varadhan, Hydrodynamics and large deviation for dimple exclusion processes, Comm. Pure Appl. Math. 42 (1989) 115-137. | MR 978701 | Zbl 0644.76001

[20] L.A. Pastur, V.A. Martchenko, The distribution of eigenvalues in certain sets of random matrices, Math. USSR-Sbornik 72 (1967) 507-536. | MR 208649 | Zbl 0152.16101

[21] W. Rudin, Real and Complex Analysis, McGraw-Hill, 1986. | Zbl 0925.00005

[22] Y. Sinai, A. Soshnikov, Central limit theorem for traces of large random symmetric matrices with independent elements, Bol. Soc. Brasil. Math. 29 (1998) 1-24. | MR 1620151 | Zbl 0912.15027

[23] D. Shlyakhtenko, Random Gaussian band matrices and freeness with amalgation, Int. Math. Res. Not. 20 (1996) 1013-1025. | MR 1422374 | Zbl 0872.15018

[24] D. Shlyakhtenko, Free Fisher information with respect to a completely positive map and cost of equivalence relations, Preprint (1999). | MR 1824202

[25] D. Voiculescu, The analogues of entropy and Fisher's information measure in free probability theory, I, Commun. Math. Phys. 155 (1993) 71-92. | MR 1228526 | Zbl 0781.60006

[26] D. Voiculescu, The analogues of entropy and Fisher's information measure in free probability theory, V: Noncommutative Hilbert transforms, Invent. Math. 132 (1) (1998) 189-227. | MR 1618636 | Zbl 0930.46053

[27] K.W. Wachter, The strong limits of random matrix spectra for sample matrices of independent elements, Ann. Probab. 6 (1978) 1-18. | MR 467894 | Zbl 0374.60039

[28] E. Wigner, On the distribution of the roots of certain symmetric matrices, Ann. Math. 67 (1958) 325-327. | MR 95527 | Zbl 0085.13203

[29] J. Wishart, The generalized product moment distribution in samples from a normal multivariate population, Biometrika 20 A (1928) 32-52. | JFM 54.0565.02