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References

  1. Bai, Z. D. Methodologies in spectral analysis of large-dimensional random matrices, a review.With comments by G. J. Rodgers and Jack W. Silverstein; and a rejoinder by the author. Statist. Sinica 9 (1999), no. 3, 611--677. MR1711663 (2000e:60044)
  2. Bai, Z. D.; Yin, Y. Q. Limit of the smallest eigenvalue of a large-dimensional sample covariance matrix. Ann. Probab. 21 (1993), no. 3, 1275--1294. MR1235416 (94j:60060)
  3. Bai, Z. D.; Silverstein, Jack W.; Yin, Y. Q. A note on the largest eigenvalue of a large-dimensional sample covariance matrix. J. Multivariate Anal. 26 (1988), no. 2, 166--168. MR0963829 (89i:62083)
  4. Bru, Marie-France. Diffusions of perturbed principal component analysis. J. Multivariate Anal. 29 (1989), no. 1, 127--136. MR0991060 (90k:62123)
  5. Cabanal Duvillard, T.; Guionnet, A. Large deviations upper bounds for the laws of matrix-valued processes and non-communicative entropies. Ann. Probab. 29 (2001), no. 3, 1205--1261. MR1872742 (2003a:60040)
  6. Capitaine, M.; Donati-Martin, C. Free Wishart processes. J. Theoret. Probab. 18 (2005), no. 2, 413--438. MR2137451 (2006e:46072)
  7. Demni, Nizar. The Laguerre process and generalized Hartman-Watson law. Bernoulli 13 (2007), no. 2, 556--580. MR2331264 (2008e:60257)
  8. Demni N.: Processus Stochastiques Matriciels, Systemesde Racines et Probabilites Non Commutatives. Thesis, Universite Pierre et Marie Curie, 2007.
  9. Donati-Martin, Catherine; Doumerc, Yan; Matsumoto, Hiroyuki; Yor, Marc. Some properties of the Wishart processes and a matrix extension of the Hartman-Watson laws. Publ. Res. Inst. Math. Sci. 40 (2004), no. 4, 1385--1412. MR2105711 (2005k:60251)
  10. Ethier, Stewart N.; Kurtz, Thomas G. Markov processes.Characterization and convergence.Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley & Sons, Inc., New York, 1986. x+534 pp. ISBN: 0-471-08186-8 MR0838085 (88a:60130)
  11. Haagerup, Uffe; Thorbjørnsen, Steen. Random matrices with complex Gaussian entries. Expo. Math. 21 (2003), no. 4, 293--337. MR2022002 (2005b:46142)
  12. Geman, Stuart. A limit theorem for the norm of random matrices. Ann. Probab. 8 (1980), no. 2, 252--261. MR0566592 (81m:60046)
  13. Graczyk, Piotr; Letac, Gérard; Massam, Hélène. The complex Wishart distribution and the symmetric group. Ann. Statist. 31 (2003), no. 1, 287--309. MR1962508 (2003m:62166)
  14. Graczyk, P.; Letac, G.; Massam, H. The hyperoctahedral group, symmetric group representations and the moments of the real Wishart distribution. J. Theoret. Probab. 18 (2005), no. 1, 1--42. MR2132270 (2006e:60021)
  15. Graczyk, P.; Vostrikova, L. The moments of Wishart processes via Itô calculus. Teor. Veroyatn. Primen. 51 (2006), no. 4, 732--751; translation in Theory Probab. Appl. 51 (2007), no. 4, 609--625 MR2338064 (2008k:62026)
  16. A Guionnet.: Random Matrices: Lectures on MacroscopicAsymptotics.Ecole d'ÈtÈ des Probabilites de Saint-Flour XXXVI2006, (Lecture Notes in Mathematics), Springer, 2008.
  17. Hiai, Fumio; Petz, Dénes. The semicircle law, free random variables and entropy.Mathematical Surveys and Monographs, 77. American Mathematical Society, Providence, RI, 2000. x+376 pp. ISBN: 0-8218-2081-8 MR1746976 (2001j:46099)
  18. Jacod, Jean; Shiryaev, Albert N. Limit theorems for stochastic processes.Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 288. Springer-Verlag, Berlin, 1987. xviii+601 pp. ISBN: 3-540-17882-1 MR0959133 (89k:60044)
  19. Katori, Makoto; Tanemura, Hideki. Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems. J. Math. Phys. 45 (2004), no. 8, 3058--3085. MR2077500 (2005g:82099)
  20. König, Wolfgang; O'Connell, Neil. Eigenvalues of the Laguerre process as non-colliding squared Bessel processes. Electron. Comm. Probab. 6 (2001), 107--114 (electronic). MR1871699 (2002j:15025)
  21. Lawi, Stephan. Hermite and Laguerre polynomials and matrix-valued stochastic processes. Electron. Commun. Probab. 13 (2008), 67--84. MR2386064 (2009a:60090)
  22. Letac, Gérard; Massam, Hélène. All invariant moments of the Wishart distribution. Scand. J. Statist. 31 (2004), no. 2, 295--318. MR2066255 (2005f:62092)
  23. Marčenko, V. A.; Pastur, L. A. Distribution of eigenvalues in certain sets of random matrices.(Russian) Mat. Sb. (N.S.) 72 (114) 1967 507--536. MR0208649 (34 #8458)
  24. Oravecz, Ferenc; Petz, Dénes. On the eigenvalue distribution of some symmetric random matrices. Acta Sci. Math. (Szeged) 63 (1997), no. 3-4, 383--395. MR1480488 (99a:60020)
  25. Pérez-Abreu, Víctor; Tudor, Constantin. Functional limit theorems for trace processes in a Dyson Brownian motion. Commun. Stoch. Anal. 1 (2007), no. 3, 415--428. MR2403859 (2009k:60216)
  26. Silverstein, Jack W. The smallest eigenvalue of a large-dimensional Wishart matrix. Ann. Probab. 13 (1985), no. 4, 1364--1368. MR0806232 (87b:60050)
  27. Voiculescu D., Dykema K.J. and Nica A.: Free RandomVariables. CRM Monographs Series, Vol. 1, 1992. MR1217253
  28. Wachter, Kenneth W. The strong limits of random matrix spectra for sample matrices of independent elements. Ann. Probability 6 (1978), no. 1, 1--18. MR0467894 (57 #7744)
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