Random matrix theory and its applications National University of Singapore, of Lecture Notes Series. Institute for Mathematical Sciences Multivariate statistics and wireless communications, Papers from the workshop held at the National University of Singapore, 2006. ,
Central limit theorems for eigenvalues in a spiked population model. Ann. Inst. Henri Poincaré Probab, Stat, vol.44, issue.3, pp.447-47407, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00129331
Silverstein: No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices, Ann. Probab, vol.26, issue.1, pp.316-345, 1998. ,
Silverstein: Exact separation of eigenvalues of large-dimensional sample covariance matrices, Ann. Probab, vol.27, issue.3, pp.1536-1555, 1999. ,
Silverstein: CLT for linear spectral statistics of large-dimensional sample covariance matrices, Ann. Probab, vol.32, issue.1A, pp.553-605, 2004. ,
Silverstein: Spectral analysis of large dimensional random matrices Springer Series in Statistics, pp.978-979, 2010. ,
Yin: Limit of the smallest eigenvalue of a largedimensional sample covariance matrix ,
Silverstein: Spectral analysis of large dimensional random matrices Springer Series in Statistics, pp.978-979, 2010. ,
Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices, The Annals of Probability, vol.33, issue.5, pp.1643-1697, 2005. ,
DOI : 10.1214/009117905000000233
Eigenvalues of large sample covariance matrices of spiked population models, Journal of Multivariate Analysis, vol.97, issue.6, pp.1382-1408, 2006. ,
DOI : 10.1016/j.jmva.2005.08.003
Universality for the largest eigenvalue of sample covariance matrices with general population, The Annals of Statistics, vol.43, issue.1, 2013. ,
DOI : 10.1214/14-AOS1281SUPP
PDEs SATISFIED BY EXTREME EIGENVALUES DISTRIBUTIONS OF GUE AND LUE, Random Matrices: Theory and Applications, vol.01, issue.01, p.1150003, 2012. ,
DOI : 10.1142/S2010326311500031
Fluctuations of the Extreme Eigenvalues of Finite Rank Deformations of Random Matrices, Electronic Journal of Probability, vol.16, issue.0, pp.1621-1662, 2011. ,
DOI : 10.1214/EJP.v16-929
URL : https://hal.archives-ouvertes.fr/hal-00505497
The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices, Advances in Mathematics, vol.227, issue.1, pp.494-521, 2011. ,
DOI : 10.1016/j.aim.2011.02.007
URL : https://hal.archives-ouvertes.fr/hal-00423593
Najim: Performance of statistical tests for single-source detection using random matrix theory. Information Theory, IEEE Transactions on, vol.57, issue.4, pp.2400-2419, 2011. ,
Asymptotic Independence in the Spectrum of the Gaussian Unitary Ensemble, Electronic Communications in Probability, vol.15, issue.0, pp.376-395, 2010. ,
DOI : 10.1214/ECP.v15-1568
URL : https://hal.archives-ouvertes.fr/hal-00556126
Repr??senta\-tions int??grales pour les polyn??mes d'Hermite et de Laguerre multiples, Annales de l???institut Fourier, vol.55, issue.6, pp.2001-2014, 2005. ,
DOI : 10.5802/aif.2148
On the principal components of sample covariance matrices, Probability Theory and Related Fields, vol.177, issue.6, 2014. ,
DOI : 10.1007/s00440-015-0616-x
Virág: Limits of spiked random matrices II. submitted, 2011. ,
Limits of spiked random matrices I. Probab. Theory Related Fields, pp.3-4795, 2013. ,
Asymptotic independence of the extreme eigenvalues of Gaussian unitary ensemble, Journal of Mathematical Physics, vol.51, issue.2, p.23514, 2010. ,
DOI : 10.1063/1.3290968
On the numerical evaluation of Fredholm determinants, Mathematics of Computation, vol.79, issue.270 ,
DOI : 10.1090/S0025-5718-09-02280-7
Increasing subsequences and the hard-to-soft edge transition in matrix ensembles, Journal of Physics A: Mathematical and General, vol.36, issue.12, pp.2963-2981, 2003. ,
DOI : 10.1088/0305-4470/36/12/307
Universal singularity at the closure of a gap in a random matrix theory, Physical Review E, vol.57, issue.4, pp.4140-4149, 1998. ,
DOI : 10.1103/PhysRevE.57.4140
Fluctuations at the edges of the spectrum of the full rank deformed GUE, Probability Theory and Related Fields, vol.155, issue.1, 2014. ,
DOI : 10.1007/s00440-015-0628-6
URL : https://hal.archives-ouvertes.fr/hal-01011501
Random matrix methods for wireless communications, 2011. ,
DOI : 10.1017/CBO9780511994746
URL : https://hal.archives-ouvertes.fr/hal-00658725
Linear operators and their spectra, volume 106 of Cambridge Studies in Advanced Mathematics, 2007. ,
Kuijlaars: A phase transition for nonintersecting Brownian motions, and the Painlevé equation, Int. Math. Res. Not. IMRN, pp.3639-3725, 2009. ,
A Graph-based Equilibrium Problem for the Limiting Distribution of Nonintersecting Brownian Motions at??Low??Temperature, Constructive Approximation, vol.10, issue.3, pp.467-512, 2010. ,
DOI : 10.1007/s00365-010-9106-7
Eigenvalues and Condition Numbers of Random Matrices, SIAM Journal on Matrix Analysis and Applications, vol.9, issue.4, pp.543-560, 1988. ,
DOI : 10.1137/0609045
Eigenvalues and Condition Numbers of Random Matrices, SIAM Journal on Matrix Analysis and Applications, vol.9, issue.4, pp.543-560, 1988. ,
DOI : 10.1137/0609045
Tracy???Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices, The Annals of Probability, vol.35, issue.2, pp.663-714, 2007. ,
DOI : 10.1214/009117906000000917
Higher transcendental functions. Vols. I, II, 1953. ,
A Universality Result for the Smallest Eigenvalues of Certain Sample Covariance Matrices, Geometric and Functional Analysis, vol.177, issue.3, pp.88-123, 2010. ,
DOI : 10.1007/s00039-010-0055-x
The spectrum edge of random matrix ensembles, Nuclear Physics B, vol.402, issue.3, pp.709-7280550, 1993. ,
DOI : 10.1016/0550-3213(93)90126-A
A Limit Theorem for the Norm of Random Matrices, The Annals of Probability, vol.8, issue.2, pp.252-2612, 1980. ,
DOI : 10.1214/aop/1176994775
Riemann-hilbert approach to gap probabilities for the bessel process. preprint, 2013. ,
Traces and determinants of linear operators, volume 116 of Operator Theory: Advances and Applications, 2000. ,
Numerical inverting of matrices of high order. II, Proc. Amer, pp.188-202, 1951. ,
DOI : 10.1090/S0002-9939-1951-0041539-X
Shape Fluctuations and Random Matrices, Communications in Mathematical Physics, vol.209, issue.2, pp.437-476, 2000. ,
DOI : 10.1007/s002200050027
components analysis, The Annals of Statistics, vol.29, issue.2, pp.295-327, 2001. ,
DOI : 10.1214/aos/1009210544
Anisotropic local laws for random matrices. to be released soon, 2014. ,
DOI : 10.1007/s00440-016-0730-4
URL : http://arxiv.org/abs/1410.3516
The Oxford handbook of random matrix theory, pp.103-134, 2011. ,
Noise Dressing of Financial Correlation Matrices, Physical Review Letters, vol.83, issue.7, p.1467, 1999. ,
DOI : 10.1103/PhysRevLett.83.1467
Almost Sure Localization of the Eigenvalues in a Gaussian Information Plus Noise Model. Application to the Spiked Models., Electronic Journal of Probability, vol.16, issue.0, pp.16-943, 1934. ,
DOI : 10.1214/EJP.v16-943
URL : https://hal.archives-ouvertes.fr/hal-00692258
Pastur: Distribution of eigenvalues in certain sets of random matrices, Mat. Sb. (N.S.), issue.114, pp.72507-536, 1967. ,
On the condition number distribution of complex wishart matrices, IEEE Transactions on Communications, vol.58, issue.6, pp.1705-1717, 2010. ,
DOI : 10.1109/TCOMM.2010.06.090328
Rank 1 real Wishart spiked model, Communications on Pure and Applied Mathematics, vol.194, issue.11, pp.1528-1638, 2012. ,
DOI : 10.1002/cpa.21415
A Random Matrix Approach to Credit Risk, PLoS ONE, vol.42, issue.5, 2014. ,
DOI : 10.1371/journal.pone.0098030.s004
Gaussian fluctuations for linear spectral statistics of large random covariance matrices, The Annals of Applied Probability, vol.26, issue.3 ,
DOI : 10.1214/15-AAP1135
URL : https://hal.archives-ouvertes.fr/hal-00861793
Numerical inverting of matrices of high order, Bulletin of the American Mathematical Society, vol.53, issue.11, pp.1021-1099, 1947. ,
DOI : 10.1090/S0002-9904-1947-08909-6
Asymptotics and special functions, Computer Science and Applied Mathematics, 1974. ,
The Tracy???Widom limit for the largest eigenvalues of singular complex Wishart matrices, The Annals of Applied Probability, vol.18, issue.2, pp.470-49007, 2008. ,
DOI : 10.1214/07-AAP454
Eigenvalue distribution of large random matrices, volume 171 of Mathematical Surveys and Monographs, 2011. ,
Universality results for the largest eigenvalues of some sample covariance matrix ensembles. Probab. Theory Related Fields, pp.3-4481, 2009. ,
Universality of covariance matrices, The Annals of Applied Probability, vol.24, issue.3, pp.935-100113, 2014. ,
DOI : 10.1214/13-AAP939
Real and complex analysis, 1987. ,
Logarithmic potentials with external fields, volume 316 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 1997. ,
Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices, Journal of Multivariate Analysis, vol.55, issue.2, pp.331-339, 1995. ,
DOI : 10.1006/jmva.1995.1083
Analysis of the Limiting Spectral Distribution of Large Dimensional Random Matrices, Journal of Multivariate Analysis, vol.54, issue.2 ,
DOI : 10.1006/jmva.1995.1058
Trace ideals and their applications, volume 120 of Mathematical Surveys and Monographs, 2005. ,
A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices, Journal of Statistical Physics, vol.108, issue.5/6, pp.1033-1056, 2002. ,
DOI : 10.1023/A:1019739414239
Random Matrices: the Distribution of the Smallest Singular Values, Geometric and Functional Analysis, vol.20, issue.2, pp.260-297, 2010. ,
DOI : 10.1007/s00039-010-0057-8
Level-spacing distributions and the Airy kernel, Communications in Mathematical Physics, vol.21, issue.1, pp.151-174, 1994. ,
DOI : 10.1007/BF02100489
Level spacing distributions and the Bessel kernel, Communications in Mathematical Physics, vol.13, issue.2, pp.289-309, 1994. ,
DOI : 10.1007/BF02099779
Limit laws for Random matrices and free products, Inventiones mathematicae, vol.67, issue.3, pp.201-220, 1991. ,
DOI : 10.1007/BF01245072
RANDOM COVARIANCE MATRICES: UNIVERSALITY OF LOCAL STATISTICS OF EIGENVALUES UP TO THE EDGE, Random Matrices: Theory and Applications, vol.01, issue.01, p.1150005, 2012. ,
DOI : 10.1142/S2010326311500055