Fluctuations de la loi empirique de grandes matrices aléatoires
Annales de l'I.H.P. Probabilités et statistiques, Volume 37 (2001) no. 3, p. 373-402
@article{AIHPB_2001__37_3_373_0,
     author = {Cabanal-Duvillard, Thierry},
     title = {Fluctuations de la loi empirique de grandes matrices al\'eatoires},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Elsevier},
     volume = {37},
     number = {3},
     year = {2001},
     pages = {373-402},
     zbl = {1016.15020},
     mrnumber = {1831988},
     language = {fr},
     url = {http://www.numdam.org/item/AIHPB_2001__37_3_373_0}
}
Cabanal-Duvillard, Thierry. Fluctuations de la loi empirique de grandes matrices aléatoires. Annales de l'I.H.P. Probabilités et statistiques, Volume 37 (2001) no. 3, pp. 373-402. http://www.numdam.org/item/AIHPB_2001__37_3_373_0/

[1] Anshelevich M., The linearization of the central limit operator in free probability theory, Probab. Theory Related Fields, à paraître. | MR 1725403 | Zbl 0983.46051

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

[3] P Biane, Processes with free increments, Math. Z. 227 (1) (1998) 143-174. | MR 1605393 | Zbl 0902.60060

[4] Biane P., Speicher R., Stochastic calculus with respect to free Brownian motion and analysis on Wigner space, Preprint. | MR 1660906 | Zbl 0919.60056

[5] Guionnet A., Fluctuations for strongly interacting random variables and Wigner's law, Preprint.

[6] K Johannson, On fluctuations of eigenvalues of random hermitian matrices, Preprint, 1995. | MR 1487983 | Zbl 1039.82504

[7] D Jonsson, Some limit theorems for the eigenvalues of a sample covariance matrix, J. Multivariate Analysis 12 (1982) 1-38. | MR 650926 | Zbl 0491.62021

[8] Młotkowski W., Free probability on algebras with infinitely many states, Preprint. | MR 1728922 | Zbl 0941.60020

[9] 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

[10] D Revuz, M Yor, Continuous Martingales and Brownian Motion, Springer, Berlin, 1994. | MR 1303781 | Zbl 0804.60001

[11] D Voiculescu, Symmetries of Some Reduced Free Product C∗-Algebras, Lecture Notes in Math., 1132, Springer-Verlag, 1985. | Zbl 0618.46048

[12] D Voiculescu, Addition of certain non-commuting random variables, J. Funct. Anal. 66 (1986) 323-346. | MR 839105 | Zbl 0651.46063

[13] D Voiculescu, Limit laws for random matrices and free products, Invent. Math. 104 (1991) 201-220. | MR 1094052 | Zbl 0736.60007

[14] D Voiculescu, K Dykema, A Nica, Free Random Variables, CRM Monographs Series, 1, Amer. Math. Soc, Providence, RI, 1992. | MR 1217253 | Zbl 0795.46049

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

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

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