.. Main-results, 122 4.2.1 General results 122 4.2.2 Second-order freeness implies fluctuations of matrix elements, p.124

G. Anderson and O. , Zeitouni A CLT for a band matrix model, Probab. Theory Rel. Fields, pp.283-338, 2005.
DOI : 10.1007/s00440-004-0422-3

G. Anderson, A. Guionnet, and O. , Zeitouni An Introduction to Random Matrices. Cambridge studies in advanced mathematics, p.118, 2009.

A. D. 'aristotile, P. Diaconis, and C. , Newman Brownian motion and the classical groups. With Probability, Statisitica and their applications: Papers in Honor of Rabii Bhattacharaya, pp.97-116, 2003.

R. Arratia and S. , The Cycle Structure of Random Permutations, The Annals of Probability, vol.20, issue.3, pp.1567-1591, 1992.
DOI : 10.1214/aop/1176989707

Z. D. Bai and J. , Silverstein CLT for linear spectral statistics of large-dimensional sample covariance matrices, Ann. Probab, vol.32, pp.533-605, 2004.

Z. D. Bai and J. W. , Silverstein Spectral analysis of large dimensional random matrices, 2009.

Z. D. Bai, X. Wang, and W. , CLT for Linear Spectral Statistics of Wigner matrices, Electronic Journal of Probability, vol.14, issue.0, pp.2391-2417, 2009.
DOI : 10.1214/EJP.v14-705

Z. D. Bai and J. , On the convergence of the spectral empirical process of Wigner matrices, Bernoulli, vol.11, issue.6, pp.1059-1092, 2005.
DOI : 10.3150/bj/1137421640

J. Baik, G. Ben-arous, and S. , 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

A. Basak and A. , Dembo Limiting spectral distribution of sums of unitary and orthogonal matrices, Electron. Commun. Probab, vol.18, issue.19, p.pp, 2013.

S. T. Belinschi, H. Bercovici, M. Capitaine, and M. Février, Outliers in the spectrum of large deformed unitarily invariant models arXiv:1207, p.2012

F. Benaych-georges, Central limit theorems for the brownian motion on large unitary groups, Bulletin de la Société mathématique de France, vol.139, issue.4, pp.593-610, 2011.
DOI : 10.24033/bsmf.2621

URL : https://hal.archives-ouvertes.fr/hal-00374929

F. Benaych-georges, Exponential bounds for the support convergence in the Single Ring Theorem, Journal of Functional Analysis, vol.268, issue.11, pp.3492-3507, 2015.
DOI : 10.1016/j.jfa.2015.03.005

URL : https://hal.archives-ouvertes.fr/hal-01069221

F. Benaych-georges, A. Guionnet, and M. , Maida Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices, Electron, Paper no, pp.1621-1662, 2011.

F. Benaych-georges, A. Guionnet, and M. , Large deviations of the extreme eigenvalues of random deformations of matrices, Probability Theory and Related Fields, vol.62, issue.1, pp.703-751, 2012.
DOI : 10.2307/1970079

URL : https://hal.archives-ouvertes.fr/hal-00505502

F. Benaych-georges, A. Guionnet, and C. , Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices, Communications in Mathematical Physics, vol.268, issue.2, pp.641-686, 2014.
DOI : 10.1007/s00220-006-0074-5

URL : https://hal.archives-ouvertes.fr/hal-00769741

F. Benaych-georges and R. N. , 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

F. Benaych-georges and R. N. , The singular values and vectors of low rank perturbations of large rectangular random matrices, Journal of Multivariate Analysis, vol.111, pp.120-135, 2012.
DOI : 10.1016/j.jmva.2012.04.019

URL : https://hal.archives-ouvertes.fr/hal-00575203

F. Benaych-georges and J. , Rochet Outliers in the Single Ring Theorem

F. Benaych-georges and J. , Rochet Fluctuations for analytic test functions in the Single Ring Theorem

F. Benaych-georges, G. Cébron, and J. , Rochet Fluctuation of matrix entries and application to outliers of elliptic matrices

C. Bordenave and M. , Capitaine Outlier eigenvalues for deformed i.i.d. random matrices

C. Bordenave and D. , Around the circular law, Probability Surveys, vol.9, issue.0, pp.1-89, 2012.
DOI : 10.1214/11-PS183

URL : https://hal.archives-ouvertes.fr/hal-00623894

É. Borel, Sur les principes de la th??orie cin??tique des gaz, Annales scientifiques de l'??cole normale sup??rieure, vol.23, pp.9-32, 1906.
DOI : 10.24033/asens.561

Y. Cao, L. Cai, C. Qiu, J. Gu, X. He et al., Jin A random matrix theoretical approach to early event detection using experimental data

M. Capitaine, C. Donati-martin, and D. , The largest eigenvalues of finite rank deformation of large Wigner matrices: Convergence and nonuniversality of the fluctuations, The Annals of Probability, vol.37, issue.1, pp.1-47, 2009.
DOI : 10.1214/08-AOP394

URL : https://hal.archives-ouvertes.fr/hal-00379900

M. Capitaine, C. Donati-martin, and D. , Central limit theorems for eigenvalues of deformations of Wigner matrices, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.48, issue.1, pp.107-133, 2012.
DOI : 10.1214/10-AIHP410

URL : https://hal.archives-ouvertes.fr/hal-00686868

M. Capitaine, C. Donati-martin, D. Féral, and M. , Free Convolution with a Semicircular Distribution and Eigenvalues of Spiked Deformations of Wigner Matrices, Electronic Journal of Probability, vol.16, issue.0, pp.1750-1792, 2011.
DOI : 10.1214/EJP.v16-934

URL : https://hal.archives-ouvertes.fr/hal-00536164

G. Cébron and T. , Kemp Fluctuations of Brownian Motions on GL N , to appear in Ann, Inst. Henri Poincaré Probab. Stat

S. Chatterjee and E. , Meckes Multivariate normal approximation using exchangeable pairs ALEA, 2008.

B. Collins, J. A. Mingo, P. Sniady, and R. , Speicher Second order freeness and fluctuations of random matrices. III. Higher order freeness and free cumulants, Doc. Math, vol.12, pp.1-70, 2007.

B. Collins and P. , Integration with Respect to the Haar Measure on Unitary, Orthogonal and Symplectic Group, Communications in Mathematical Physics, vol.264, issue.3, pp.773-795, 2006.
DOI : 10.1007/s00220-006-1554-3

B. Collins and M. , Borel theorems for random matrices from the classical compact symmetric spaces, The Annals of Probability, vol.36, issue.3, pp.876-895, 2008.
DOI : 10.1214/07-AOP341

B. Collins and P. , Integration with Respect to the Haar Measure on Unitary, Orthogonal and Symplectic Group, Communications in Mathematical Physics, vol.264, issue.3, pp.773-795, 2006.
DOI : 10.1007/s00220-006-1554-3

P. Diaconis and M. , Shahshahani On the eigenvalues of random matrices, Studies in applied probability, J. Appl. Probab, pp.31-49, 1994.

P. Diaconis and S. , Evans Linear functionals of eigenvalues of random matrices, Transactions of the American Mathematical Society, vol.353, issue.07, pp.2615-2633, 2001.
DOI : 10.1090/S0002-9947-01-02800-8

B. Duplantier, R. Rhodes, S. Sheffield, and V. , Vargas Log-correlated Gaussian fields: an overview, arXiv

J. Feinberg and A. Zee, Non-gaussian non-hermitian random matrix theory: Phase transition and addition formalism, Nuclear Physics B, vol.501, issue.3, pp.643-669, 1997.
DOI : 10.1016/S0550-3213(97)00419-7

D. Féral and S. , The Largest Eigenvalue of Rank One Deformation of Large Wigner Matrices, Communications in Mathematical Physics, vol.163, issue.1, pp.185-228, 2007.
DOI : 10.1007/s00220-007-0209-3

Y. V. Fyodorov and H. Sommers, Statistics of S-matrix poles in few-channel chaotic scattering: Crossover from isolated to overlapping resonances, Journal of Experimental and Theoretical Physics Letters, vol.63, issue.12, pp.1026-1030, 1996.
DOI : 10.1134/1.567120

Y. V. Fyodorov and H. , Sommers Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering: Random matrix approach for systems with broken time reversal invariance, J. Math. Phys, vol.38, 1918.

Y. V. Fyodorov and B. A. , Systematic Analytical Approach to Correlation Functions of Resonances in Quantum Chaotic Scattering, Physical Review Letters, vol.6, issue.1, pp.65-68, 1999.
DOI : 10.1063/1.1704292

Y. V. Fyodorov and H. , Random matrices close to Hermitian or unitary: overview of methods and results, Journal of Physics A: Mathematical and General, vol.36, issue.12, pp.3303-3347, 2003.
DOI : 10.1088/0305-4470/36/12/326

A. Guionnet, M. Krishnapur, and O. , The single ring theorem, Annals of Mathematics, vol.174, issue.2, pp.1189-1217, 2011.
DOI : 10.4007/annals.2011.174.2.10

A. Guionnet and O. , Support convergence in the single ring theorem, Probability Theory and Related Fields, vol.36, issue.3-4, pp.661-675, 2012.
DOI : 10.1088/0305-4470/36/12/331

X. He, Q. Ai, C. Qiu, W. Huang, L. Piao et al., Liu A Big Data architecture design for smart grids based on random matrix theory

F. Hiai and D. , Petz The semicircle law, free random variables, and entropy, Amer. Math. Soc., Mathematical Surveys and Monographs, vol.77, 2000.

T. Jiang, How many entries of a typical orthogonal matrix can be approximated by independent normals?, The Annals of Probability, vol.34, issue.4, pp.1497-1529, 2006.
DOI : 10.1214/009117906000000205

K. Johansson, On the fluctuations of eigenvalues of random Hermitian matrices . Duke Math, J, vol.91, pp.151-204, 1998.

I. M. Johnstone, On the distribution of the largest eigenvalue in principal components analysis, Ann. Statist, vol.29, p.295327, 2001.

D. Jonsson, Some limit theorems for the eigenvalues of a sample covariance matrix, Journal of Multivariate Analysis, vol.12, issue.1, pp.1-38, 1982.
DOI : 10.1016/0047-259X(82)90080-X

A. M. Khorunzhy, B. A. Khoruzhenko, and L. A. , Asymptotic properties of large random matrices with independent entries, Journal of Mathematical Physics, vol.2, issue.10, pp.5033-5060, 1996.
DOI : 10.1016/0003-4916(81)90007-5

A. Knowles and J. , The Isotropic Semicircle Law and Deformation of Wigner Matrices, Communications on Pure and Applied Mathematics, vol.62, issue.1, pp.1663-1750, 2013.
DOI : 10.2307/1970079

A. Knowles and J. , The outliers of a deformed Wigner matrix, The Annals of Probability, vol.42, issue.5, pp.1980-2031, 2014.
DOI : 10.1214/13-AOP855

T. Lévy and M. , Central limit theorem for the heat kernel measure on the unitary group, Journal of Functional Analysis, vol.259, issue.12, pp.3163-3204, 2010.
DOI : 10.1016/j.jfa.2010.08.005

A. Lytova and L. , Pastur Central limit theorem for linear eigenvalue statistics of random matrices with independent entries, pp.1778-1840, 2009.

J. A. Mingo and A. , Nica Annular noncrossing permutations and partitions, and second-order asymptotics for random matrices, Int. Math. Res. Not, issue.28, pp.1413-1460, 2004.

J. A. Mingo, P. Sniady, and R. Speicher, Second order freeness and fluctuations of random matrices: II. Unitary random matrices, Advances in Mathematics, vol.209, issue.1, pp.212-240, 2007.
DOI : 10.1016/j.aim.2006.05.003

J. A. Mingo and R. , Second order freeness and fluctuations of random matrices: I. Gaussian and Wishart matrices and cyclic Fock spaces, Journal of Functional Analysis, vol.235, issue.1, pp.226-270, 2006.
DOI : 10.1016/j.jfa.2005.10.007

J. A. Mingo, P. Sniady, and R. Speicher, Second order freeness and fluctuations of random matrices: II. Unitary random matrices, Advances in Mathematics, vol.209, issue.1, pp.212-240, 2007.
DOI : 10.1016/j.aim.2006.05.003

A. Naumov, Elliptic law for real random matrices

H. Nguyen and S. O-'rourke, The Elliptic Law, International Mathematics Research Notices, vol.2015, issue.17, pp.7620-7689
DOI : 10.1093/imrn/rnu174

A. Nica and R. , Speicher Lectures on the combinatorics of free probability, 2006.

S. O-'rourke and D. , Renfrew Low rank perturbations of large elliptic random matrices, Electron, J. Probab, vol.19, issue.65, p.pp, 2014.

S. O-'rourke and D. , Renfrew Central limit theorem for linear eigenvalue statistics of elliptic random matrices

S. O-'rourke and P. , Matchett Wood Spectra of nearly Hermitian random matrices

S. O-'rourke, D. Renfrew, and A. , Soshnikov On fluctuations of matrix entries of regular functions of Wigner matrices with non-identically distributed entries, J. Theoret. Probab, vol.26, issue.3, pp.750-780, 2013.

S. Péché, The largest eigenvalue of small rank perturbations of Hermitian random matrices, Prob. Theory Relat. Fields, pp.127-173, 2006.

Y. Peres and B. , Virág Zeros of the i.i.d. Gaussian power series: a confor-mally invariant determinantal process, Acta. Math, pp.1-35, 2005.

A. Pizzo, D. Renfrew, and A. Soshnikov, On finite rank deformations of Wigner matrices, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.49, issue.1
DOI : 10.1214/11-AIHP459

A. Pizzo, D. Renfrew, and A. , Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices, Journal of Statistical Physics, vol.9, issue.2, pp.550-591, 2012.
DOI : 10.1137/1109011

B. Rider and J. W. , Gaussian fluctuations for non-Hermitian random matrix ensembles, The Annals of Probability, vol.34, issue.6, pp.2118-2143, 2006.
DOI : 10.1214/009117906000000403

B. Rider and B. , Virág The noise in the circular law and the Gaussian free field, Int. Math. Res. Not. IMRN, issue.2, 2007.

M. Rudelson and R. , Invertibility of random matrices: Unitary and orthogonal perturbations, Journal of the American Mathematical Society, vol.27, issue.2, pp.293-338, 2014.
DOI : 10.1090/S0894-0347-2013-00771-7

M. Shcherbina, Central Limit Theorem for Linear Eigenvalue Statistics of the Wigner and Sample Covariance Random Matrices, Journal of Mathematical Physics Analysis Geometry, vol.7, issue.2, pp.176-192, 2011.

Y. Sinai and A. , Central limit theorem for traces of large random symmetric matrices with independent matrix elements, Boletim da Sociedade Brasileira de Matem???tica, vol.177, issue.No. 4, pp.1-24, 1998.
DOI : 10.1007/BF01028434

H. Sommers, A. Crisanti, H. Sompolinsky, and Y. , Spectrum of Large Random Asymmetric Matrices, Physical Review Letters, vol.36, issue.19, pp.1895-1899, 1988.
DOI : 10.1103/PhysRevA.36.4922

C. Zhang and R. C. , Qiu Data Modeling with Large Random Matrices in a Cognitive Radio Network Testbed: Initial Experimental Demonstrations with 70 Nodes