@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}, publisher = {Elsevier}, volume = {38}, number = {3}, year = {2002}, mrnumber = {1899457}, zbl = {0995.60028}, language = {en}, url = {http://archive.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 - http://archive.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 http://archive.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. http://archive.numdam.org/item/AIHPB_2002__38_3_341_0/
[1] On the asymptotic distribution of eigenvalues of random matrices, J. Math. Anal. Appl. 20 (1967) 262-268. | MR | Zbl
,[2] Methodologies in spectral analysis of large dimensional random matrices: a review, Statistica Sinica 9 (1999) 611-661. | MR | Zbl
,[3] Large deviations for Wigner's law and Voiculescu's non-commutative entropy, Probab. Theory Related Fields 108 (4) (1997) 517-542. | MR | Zbl
, ,[4] Large deviations from the circular law, ESAIM Probab. Statist. 2 (1998) 123-134. | Numdam | MR | Zbl
, ,[5] Some remarks on the Wigner distribution, Teor. Mat. Fiz. 17 (1973) 1163-1171. | MR | Zbl
,[6] Free brownian motion, free stochastic calculus and random matrices, in: (Ed.), Free Probability Theory, Fields Institute Communication, 12, American Math. Soc. , 1997, pp. 1-19. | MR | Zbl
,[7] Calcul stochastique non-commutatif, in: Saint Flour 1993, Lect. Notes in Math., 1608, Springer, Berlin, 1995, pp. 1-96. | MR | Zbl
,[8] Limit theorems for random matrices, Markov Proc. Related Fields 4 (1998) 175-197. | MR | Zbl
, ,[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] Wigner's semicircle law for band matrices, Random Operators Stochastic Equations 1 (1993) 279-286. | MR | Zbl
, ,[12] Large Deviations Techniques and Applications, Jones and Bartlett Publishers, 1993. | MR | Zbl
, ,[13] Eigenvalues density of the Wishart matrix and large deviations, Infinite Dimensional Anal. Quantum Prob. 1 (1998) 633-646. | MR | Zbl
, ,[14] Concentration of the spectral measure for large matrices, Elec. Comm. Prob. 5 (2000) 14. | MR | Zbl
, ,[15] A. Guionnet, O. Zeitouni, Large deviations asymptotics for spherical integrals, J. Funct. Anal., in press. | MR | Zbl
[16] Asymptotic properties of large random matrices with independent entries, J. Math. Phys. 37 (1996) 5033-5060. | MR | Zbl
, , ,[17] The large n-limit in statistical mechanics and the spectral theory of disordered systems phase, Transition and Critical Phenomena 15 (1992) 73-239.
, , , ,[18] On fluctuations of eigenvalues of random Hermitian matrices, Duke Math. J. 91 (1998) 151-204. | MR | Zbl
,[19] Hydrodynamics and large deviation for dimple exclusion processes, Comm. Pure Appl. Math. 42 (1989) 115-137. | MR | Zbl
, , ,[20] The distribution of eigenvalues in certain sets of random matrices, Math. USSR-Sbornik 72 (1967) 507-536. | MR | Zbl
, ,[21] Real and Complex Analysis, McGraw-Hill, 1986. | Zbl
,[22] Central limit theorem for traces of large random symmetric matrices with independent elements, Bol. Soc. Brasil. Math. 29 (1998) 1-24. | MR | Zbl
, ,[23] Random Gaussian band matrices and freeness with amalgation, Int. Math. Res. Not. 20 (1996) 1013-1025. | MR | Zbl
,[24] D. Shlyakhtenko, Free Fisher information with respect to a completely positive map and cost of equivalence relations, Preprint (1999). | MR
[25] The analogues of entropy and Fisher's information measure in free probability theory, I, Commun. Math. Phys. 155 (1993) 71-92. | MR | Zbl
,[26] 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 | Zbl
,[27] The strong limits of random matrix spectra for sample matrices of independent elements, Ann. Probab. 6 (1978) 1-18. | MR | Zbl
,[28] On the distribution of the roots of certain symmetric matrices, Ann. Math. 67 (1958) 325-327. | MR | Zbl
,[29] The generalized product moment distribution in samples from a normal multivariate population, Biometrika 20 A (1928) 32-52. | JFM
,