no. 3
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) no. 3, pp. 341-384 
@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},
     pages = {341--384},
     year = {2002},
     publisher = {Elsevier},
     volume = {38},
     number = {3},
     mrnumber = {1899457},
     zbl = {0995.60028},
     language = {en},
     url = {https://www.numdam.org/item/AIHPB_2002__38_3_341_0/}
}
TY  - JOUR
AU  - Guionnet, Alice
TI  - Large deviations upper bounds and central limit theorems for non-commutative functionals of gaussian large random matrices
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2002
SP  - 341
EP  - 384
VL  - 38
IS  - 3
PB  - Elsevier
UR  - https://www.numdam.org/item/AIHPB_2002__38_3_341_0/
LA  - en
ID  - AIHPB_2002__38_3_341_0
ER  - 
%0 Journal Article
%A Guionnet, Alice
%T Large deviations upper bounds and central limit theorems for non-commutative functionals of gaussian large random matrices
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2002
%P 341-384
%V 38
%N 3
%I Elsevier
%U https://www.numdam.org/item/AIHPB_2002__38_3_341_0/
%G en
%F 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) no. 3, pp. 341-384. https://www.numdam.org/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. | Zbl | MR

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

[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. | Zbl | MR

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

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

[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. | Zbl | MR

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

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

[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

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

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

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

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

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

[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. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl | MR

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

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

[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. | Zbl | MR

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

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

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

[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. | Zbl | MR

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

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

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