Fluctuations de la loi empirique de grandes matrices aléatoires

 Access to full text

 Full (PDF)

1. [1] Anshelevich M., The linearization of the central limit operator in free probability theory, Probab. Theory Related Fields, à paraître. Zbl0983.46051MR1725403
2. [2] L Arnold, On the asymptotic distribution of eigenvalues of random matrices, J. Math. Anal. Appl.20 (1967) 262-268. Zbl0246.60029MR217833
3. [3] P Biane, Processes with free increments, Math. Z.227 (1) (1998) 143-174. Zbl0902.60060MR1605393
4. [4] Biane P., Speicher R., Stochastic calculus with respect to free Brownian motion and analysis on Wigner space, Preprint. Zbl0919.60056MR1660906
5. [5] Guionnet A., Fluctuations for strongly interacting random variables and Wigner's law, Preprint. 
6. [6] K Johannson, On fluctuations of eigenvalues of random hermitian matrices, Preprint, 1995. Zbl0820.57001
7. [7] D Jonsson, Some limit theorems for the eigenvalues of a sample covariance matrix, J. Multivariate Analysis12 (1982) 1-38. Zbl0491.62021MR650926
8. [8] Młotkowski W., Free probability on algebras with infinitely many states, Preprint. Zbl0941.60020
9. [9] L.A Pastur, V.A Martchenko, The distribution of eigenvalues in certain sets of random matrices, Math. USSR-Sbornik72 (1967) 507-536. Zbl0152.16101MR208649
10. [10] D Revuz, M Yor, Continuous Martingales and Brownian Motion, Springer, Berlin, 1994. Zbl0804.60001MR1303781
11. [11] D Voiculescu, Symmetries of Some Reduced Free Product C∗-Algebras, Lecture Notes in Math., 1132, Springer-Verlag, 1985. Zbl0618.46048
12. [12] D Voiculescu, Addition of certain non-commuting random variables, J. Funct. Anal.66 (1986) 323-346. Zbl0651.46063MR839105
13. [13] D Voiculescu, Limit laws for random matrices and free products, Invent. Math.104 (1991) 201-220. Zbl0736.60007MR1094052
14. [14] D Voiculescu, K Dykema, A Nica, Free Random Variables, CRM Monographs Series, 1, Amer. Math. Soc, Providence, RI, 1992. Zbl0795.46049MR1217253
15. [15] K.W Wachter, The strong limits of random matrix spectra for sample matrices of independant elements, Ann. Probab.6 (1978) 1-18. Zbl0374.60039MR467894
16. [16] E Wigner, On the distribution of the roots of certain symmetric matrices, Ann. Math.67 (1958) 325-327. Zbl0085.13203MR95527
17. [17] J Wishart, The generalized product moment distribution in samples from a normal multivariate population, Biometrika20 A (1928) 32-52. Zbl54.0565.02JFM54.0565.02

1. Shurong Zheng, Central limit theorems for linear spectral statistics of large dimensional F-matrices
2. A. Dembo, A. Guionnet, O. Zeitouni, Moderate deviations for the spectral measure of certain random matrices