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References

  1. G.W. Anderson, A. Guionnet, O. Zeitouni. An introduction to random matrices. Cambridge Studies in Advanced Mathematics, 118. Cambridge University Press, Cambridge, 2010. xiv+492 pp. ISBN: 978-0-521-19452-5 MR2760897
  2. Z. D. Bai, J.W. Silverstein. No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices. Ann. Probab. 26 (1998), no. 1, 316--345. MR1617051 (99b:60041)
  3. Z. D. Bai, J.W. Silverstein. CLT for linear spectral statistics of large-dimensional sample covariance matrices. Ann. Probab. 32 (2004), no. 1A, 553--605. MR2040792 (2005b:60046)
  4. Z. D. Bai, J.W. Silverstein. Spectral analysis of large dimensional random matrices. Second edition. Springer Series in Statistics. Springer, New York, 2010. xvi+551 pp. ISBN: 978-1-4419-0660-1 MR2567175 (2011d:60014)
  5. Z. D. Bai, J. Yao. On the convergence of the spectral empirical process of Wigner matrices. Bernoulli 11 (2005), no. 6, 1059--1092. MR2189081 (2006g:60034)
  6. Z. D. Bai, Y.Q. Yin. Necessary and sufficient conditions for almost sure convergence of the largest eigenvalue of a Wigner matrix. Ann. Probab. 16 (1988), no. 4, 1729--1741. MR0958213 (90a:60069)
  7. Z. D. Bai, J. Yao. Central limit theorems for eigenvalues in a spiked population model. Ann. Inst. Henri Poincaré Probab. Stat. 44 (2008), no. 3, 447--474. MR2451053 (2009j:60042)
  8. Z. D. Bai, X. Wang, W. Zhou. CLT for linear spectral statistics of Wigner matrices. Electron. J. Probab. 14 (2009), no. 83, 2391--2417. MR2556016 (2010m:60015)
  9. J. Baik, G. Ben Arous, S. Péché. Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices. Ann. Probab. 33 (2005), no. 5, 1643--1697. MR2165575(2006g:15046)
  10. F. Benaych-Georges, R. Rao Nadakuditi. The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices. Adv. Math. 227 (2011), no. 1, 494--521. MR2782201
  11. F. Benaych-Georges, A. Guionnet and M. Maïda. Large deviations of extreme eigenvalues of finite rank deformations of deterministic matrices. Probab. Theory Related Fields. To appear (2011).
  12. M. Capitaine, C. Donati-Martin, D. Féral. The largest eigenvalues of finite rank deformation of large Wigner matrices: convergence and nonuniversality of the fluctuations. Ann. Probab. 37 (2009), no. 1, 1--47. MR2489158 (2011d:15055)
  13. M. Capitaine, C. Donati-Martin, D. Féral. Central limit theorems for eigenvalues of deformations of Wigner matrices. Ann. Inst. Henri Poincaré Probab. Stat. To appear (2011).
  14. P. Deift, D. Gioev. Universality at the edge of the spectrum for unitary, orthogonal, and symplectic ensembles of random matrices. Comm. Pure Appl. Math. 60 (2007), no. 6, 867--910. MR2306224 (2008e:60089)
  15. L. Erdös, B. Schlein, H.-T. Yau. Wegner estimate and level repulsion for Wigner random matrices. Int. Math. Res. Not. IMRN 2010, no. 3, 436--479. MR2587574 (2011h:60016)
  16. L. Erdös, H.T. Yau and J. Yin. Bulk universality for generalized Wigner matrices. Preprint.
  17. L. Erdös, B. Schlein, H.-T. Yau. The local relaxation flow approach to universality of the local statistics for random matrices. Ann. Inst. Henri Poincaré Probab. Stat. To appear (2011).
  18. D. Féral, S. Péché. The largest eigenvalue of rank one deformation of large Wigner matrices. Comm. Math. Phys. 272 (2007), no. 1, 185--228. MR2291807 (2008a:82031)
  19. D. Féral, S. Péché. The largest eigenvalues of sample covariance matrices for a spiked population: diagonal case. J. Math. Phys. 50 (2009), no. 7. MR2548630 (2010j:62167)
  20. P. J. Forrester. The spectrum edge of random matrix ensembles. Nuclear Phys. B 402 (1993), no. 3, 709--728. MR1236195 (94h:82031)
  21. A. Guionnet. Large deviations upper bounds and central limit theorems for non-commutative functionals of Gaussian large random matrices. Ann. Inst. H. Poincaré Probab. Stat. 38 (2002), no. 3, 341--384. MR1899457(2003a:60042)
  22. A. Guionnet. Large random matrices: lectures on macroscopic asymptotics. Lectures from the 36th Probability Summer School held in Saint-Flour, 2006. Lecture Notes in Mathematics, 1957. Springer-Verlag, Berlin, 2009. xii+294 pp. ISBN: 978-3-540-69896-8 MR2498298(2010d:60018)
  23. A. Guionnet, E. Maurel-Segala. Combinatorial aspects of matrix models. ALEA Lat. Am. J. Probab. Math. Stat. 1 (2006), 241--279. MR2249657(2007g:05087)
  24. D. L. Hanson, F. T. Wright. A bound on tail probabilities for quadratic forms in independent random variables. Ann. Math. Statist. 42 (1971) 1079--1083. MR0279864 (43 #5585)
  25. J. Galambos. The asymptotic theory of extreme order statistics. The theory and applications of reliability, with emphasis on Bayesian and nonparametric methods (Conf., Univ. South Florida, Tampa, Fla., 1975), Vol. I, pp. 151--164. Academic Press, New York, 1977. MR0455075 (56 #13315)
  26. E. J. Gumbel. Statistics of extremes. Columbia University Press, New York 1958 xx+375 pp. MR0096342 (20 #2826)
  27. A. Intarapanich, P. Shaw, A. Assawamakin, P. Wangkumhang, C. Ngamphiw, K. Chaichoompu, J. Piriyapongsa and S.Tongsima. Iterative pruning PCA improves resolution of highly structured populations Preprint.
  28. K. Johansson. On fluctuations of eigenvalues of random Hermitian matrices. Duke Math. J. 91 (1998), no. 1, 151--204. MR0096342 (2000m:82026)
  29. S. Kritchman, B. Nadler. Non-parametric detection of the number of signals: Hypothesis testing and random matrix theory. IEEE Trans. Signal Process. 57 (2009), no. 10, 3930--3941. MR2683143 (2011d:94034)
  30. A. Lytova, L. Pastur. Central limit theorem for linear eigenvalue statistics of random matrices with independent entries. Ann. Probab. 37 (2009), no. 5, 1778--1840. MR2561434(2011c:60024)
  31. C. Mâle. Norm of polynomials in large random and deterministic matrices. Probab. Theory Related Fields. To appear (2011).
  32. V. A. Marčenko, L. A. Pastur. Distribution of eigenvalues in certain sets of random matrices. (Russian) Mat. Sb. (N.S.) 72 (114) 1967 507--536. MR0208649 (34 #8458)
  33. T. Nagao, M. Wadati. Correlation functions of random matrix ensembles related to classical orthogonal polynomials. III. J. Phys. Soc. Japan 61 (1992), no. 6, 1910--1918. MR1177976 (93k:82029)
  34. N. Patterson, A. Price and D. Reich. Population Structure and Eigenanalysis. Preprint.
  35. L. Pastur. Limiting laws of linear eigenvalue statistics for Hermitian matrix models. J. Math. Phys. 47 (2006), no. 10, 103303, 22 pp. MR2268864 (2008a:82040)
  36. S. Péché. The largest eigenvalue of small rank perturbations of Hermitian random matrices. Probab. Theory Related Fields 134 (2006), no. 1, 127--173. MR2221787 (2007d:15041)
  37. S. Péché. Universality results for the largest eigenvalues of some sample covariance matrix ensembles. Probab. Theory Related Fields 143 (2009), no. 3-4, 481--516. MR2475670 (2009m:60013)
  38. F. Perra, R. Garello and M. Spirito. Probability of Missed Detection in Eigenvalue Ratio Spectrum Sensing. Preprint.
  39. A. Ruzmaikina. Universality of the edge distribution of eigenvalues of Wigner random matrices with polynomially decaying distributions of entries. Comm. Math. Phys. 261 (2006), no. 2, 277--296. MR2191882(2006k:82093)
  40. B. Schlein. Private communication (2010)
  41. A. Soshnikov. Universality at the edge of the spectrum in Wigner random matrices. Comm. Math. Phys. 207 (1999), no. 3, 697--733. MR1727234 (2001i:82037)
  42. T. Tao, V. Vu. Random matrices: universality of local eigenvalue statistics up to the edge. Comm. Math. Phys. 298 (2010), no. 2, 549--572. MR2669449 (2011f:60012)
  43. T. Tao and V. Vu. Random Matrices: Localization of the eigenvalues and the necessity of four moments. Preprint.
  44. C.A. Tracy, H. Widom. Level-spacing distributions and the Airy kernel. Comm. Math. Phys. 159 (1994), no. 1, 151--174. MR1257246 (95e:82003)
  45. C.A. Tracy, H. Widom. On orthogonal and symplectic matrix ensembles. Comm. Math. Phys. 177 (1996), no. 3, 727--754. MR1385083 (97a:82055)
  46. D. Wang. The largest sample eigenvalue distribution in the rank 1 quaternionic spiked model of Wishart ensemble. Ann. Probab. 37 (2009), no. 4, 1273--1328. MR2546746 (2011a:60036)
  47. M. Shcherbina. Edge universality for orthogonal ensembles of random matrices. J. Stat. Phys. 136 (2009), no. 1, 35--50. MR2525225 (2011b:82036)


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