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

G. Anderson and O. , Zeitouni A CLT for a band matrix model, Probab. Theory Rel. Fields, pp.283-338, 2005.

A. Auffinger, G. Ben-arous, and S. , Poisson convergence for the largest eigenvalues of heavy tailed random matrices, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.45, issue.3, pp.589-610, 2009.
DOI : 10.1214/08-AIHP188

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

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, 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

S. Belinschi, A. Dembo, and A. , Spectral Measure of Heavy Tailed Band and Covariance Random Matrices, Communications in Mathematical Physics, vol.268, issue.2, pp.1023-1055, 2009.
DOI : 10.1007/s00220-009-0822-4

G. B. Arous and K. , Dang On fluctuations of eigenvalues of random permutation matrices

G. B. Arous and A. , The Spectrum of Heavy Tailed Random Matrices, Communications in Mathematical Physics, vol.268, issue.2, pp.715-751, 2008.
DOI : 10.1007/s00220-007-0389-x

F. Benaych-georges and S. , Péché Localization and delocalization for heavy tailed band matrices, To appear in Ann. Inst. Henri Poincaré Probab

N. H. Bingham, C. M. Goldie, and J. L. Teugels, Regular variation, 1989.
DOI : 10.1017/CBO9780511721434

C. Bordenave and A. , Guionnet Localization and delocalization of eigenvectors for heavy-tailed random matrices, arxiv

C. Bordenave, P. Caputo, and D. , Chafa¨?Chafa¨? Spectrum of large random reversible Markov chains: heavy-tailed weights on the complete graph, pp.1544-1590

C. Bordenave, P. Caputo, and D. , Spectrum of Non-Hermitian Heavy Tailed Random Matrices, Communications in Mathematical Physics, vol.20, issue.1, pp.513-560, 2011.
DOI : 10.1007/s00220-011-1331-9
URL : https://hal.archives-ouvertes.fr/hal-00490516

P. Cizeau and J. Bouchaud, Theory of Lévy matrices Phys, Rev. E, vol.50, 1994.

P. Deift, Orthogonal polynomials and random matrices: a Riemann-Hilbert approach, Courant Lecture Notes in Mathematics, vol.3, 1999.
DOI : 10.1090/cln/003

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

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

I. Dumitriu, T. Johnson, S. Pal, and E. , Paquette Functional limit theorems for random regular graphs, Probab. Theory Related Fields, pp.1-55, 2012.

L. Erdös, B. Schlein, and H. , Yau Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices, p.37, 2009.

L. Erdös, H. T. Yau, and J. , Rigidity of eigenvalues of generalized Wigner matrices, Advances in Mathematics, vol.229, issue.3, pp.1435-1515, 2012.
DOI : 10.1016/j.aim.2011.12.010

A. Guionnet, Large random matrices: lectures on macroscopic asymptotics Lectures from the 36th Probability Summer School held in Saint-Flour, Lecture Notes in Mathematics, 1957.

A. Guionnet and E. , Second order asymptotics for matrix models, The Annals of Probability, vol.35, issue.6, pp.2160-2212, 2007.
DOI : 10.1214/009117907000000141
URL : https://hal.archives-ouvertes.fr/hal-00192328

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

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.37, issue.10, pp.5033-5060, 1996.
DOI : 10.1063/1.531589

O. Khorunzhy, M. Shcherbina, and V. , Eigenvalue distribution of large weighted random graphs, Journal of Mathematical Physics, vol.45, issue.4, pp.1648-1672, 2004.
DOI : 10.1063/1.1667610

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

J. 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

A. Mirlin and Y. , Universality of level correlation function of sparse random matrices, Journal of Physics A: Mathematical and General, vol.24, issue.10, pp.2273-2286, 1991.
DOI : 10.1088/0305-4470/24/10/016

G. Samorodnitsky and M. , Taqqu Stable non-Gaussian random processes. Stochastic models with infinite variance. Stochastic Modeling, 1994.

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.

M. Shcherbina and B. Tirozzi, Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs, Journal of Mathematical Physics, vol.51, issue.2, pp.23523-23543, 2010.
DOI : 10.1063/1.3299297

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/BF01245866

T. Tao and V. , Random matrices: Universality of local eigenvalue statistics, Acta Mathematica, vol.206, issue.1, pp.127-204, 2011.
DOI : 10.1007/s11511-011-0061-3

V. Vengerovsky, Asymptotics of the correlator of an ensemble of sparse random matrices, (Russian) Mat. Fiz. Anal. Geom, vol.11, issue.2, pp.135-160, 2004.

I. Zakharevich, A Generalization of Wigner???s Law, Communications in Mathematical Physics, vol.67, issue.2, pp.403-414, 2006.
DOI : 10.1007/s00220-006-0074-5