M. Aizenman, R. Sims, and S. Warzel, Stability of the absolutely continuous spectrum of random Schrödinger operators on tree graphs. Probab. Theory Related Fields, pp.363-394, 2006.

D. Aldous and J. M. Steele, The Objective Method: Probabilistic Combinatorial Optimization and Local Weak Convergence, Probability on discrete structures, pp.1-72, 2004.
DOI : 10.1007/978-3-662-09444-0_1

URL : http://www-stat.wharton.upenn.edu/~steele/Publications/PDF/OMSurvey.pdf

G. W. Anderson, A. Guionnet, and O. Zeitouni, An introduction to random matrices, volume 118 of Cambridge Studies in Advanced Mathematics, 2010.

G. , B. Arous, and A. Guionnet, Large deviations for Wigner's law and Voiculescu's non-commutative entropy. Probabilty theory and related fields, pp.517-542, 1997.
DOI : 10.1007/s004400050119

E. Artin, The gamma function. Translated by Michael Butler, Athena Series: Selected Topics in Mathematics, 1964.

F. Augeri, Large deviations principle for the largest eigenvalue of Wigner matrices without Gaussian tails, Electronic Journal of Probability, vol.21, p.49, 2016.
DOI : 10.1214/16-EJP4146

URL : http://doi.org/10.1214/16-ejp4146

]. F. Augeri, On the large deviations of traces of random matrices, 2016.

Z. Bai and J. W. Silverstein, Spectral analysis of large dimensional random matrices, 2010.
DOI : 10.1007/978-1-4419-0661-8

Z. D. Bai and J. Yao, 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

Z. D. Bai and Y. Q. Yin, Necessary and Sufficient Conditions for Almost Sure Convergence of the Largest Eigenvalue of a Wigner Matrix, The Annals of Probability, vol.16, issue.4, pp.1729-1741, 1988.
DOI : 10.1214/aop/1176991594

J. Baik, G. B. Arous, and S. Péché, 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

J. Baik, P. Deift, and K. Johansson, On the distribution of the length of the longest increasing subsequence of random permutations, Journal of the American Mathematical Society, vol.12, issue.04, pp.1119-1178, 1999.
DOI : 10.1090/S0894-0347-99-00307-0

D. Bakry, I. Gentil, and M. Ledoux, Analysis and geometry of Markov diffusion operators, of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 2014.
DOI : 10.1007/978-3-319-00227-9

URL : https://hal.archives-ouvertes.fr/hal-00929960

F. Barthe, P. Cattiaux, and C. Roberto, Concentration for independent random variables with heavy tails, AMRX Appl. Math. Res. Express, issue.2, pp.39-60, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00004959

S. T. Belinschi, H. Bercovici, and M. Février, Outliers in the spectrum of large deformed unitarily invariant models. to appear in the Annals of Probability
URL : https://hal.archives-ouvertes.fr/hal-01981163

G. B. Arous, A. Dembo, and A. Guionnet, Aging of spherical spin glasses. Probab. Theory Related Fields, pp.1-67, 2001.

G. , B. Arous, and A. Guionnet, The spectrum of heavy tailed random matrices, Comm. Math. Phys, vol.278, issue.3, pp.715-751, 2008.

F. Benaych-georges, A. Guionnet, and M. Maida, Large deviations of the extreme eigenvalues of random deformations of matrices. Probab. Theory Related Fields, pp.3-4703, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00505502

F. Benaych-georges, A. Guionnet, and C. Male, 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. R. Nadakuditi, 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

H. Bercovici and D. Voiculescu, Indiana University Mathematics Journal, vol.42, issue.3, pp.733-773, 1993.
DOI : 10.1512/iumj.1993.42.42033

R. Bhatia, Matrix analysis, volume 169 of Graduate Texts in Mathematics, 1997.

P. Biane, On the free convolution with a semi-circular distribution, Indiana University Mathematics Journal, vol.46, issue.3, pp.705-718, 1997.
DOI : 10.1512/iumj.1997.46.1467

P. Billingsley, Convergence of probability measures Wiley Series in Probability and Statistics: Probability and Statistics, 1999.

S. Bobkov and M. Ledoux, Poincaré's inequalities and Talagrand's concentration phenomenon for the exponential distribution. Probab. Theory Related Fields, pp.383-400, 1997.

S. G. Bobkov, Isoperimetric and Analytic Inequalities for Log-Concave Probability Measures, The Annals of Probability, vol.27, issue.4, pp.1903-1921, 1999.
DOI : 10.1214/aop/1022874820

S. G. Bobkov and M. Ledoux, From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities, Geometric and Functional Analysis, vol.10, issue.5, pp.1028-1052, 2000.
DOI : 10.1007/PL00001645

URL : http://www-sv.cict.fr/lsp/Ledoux/BL3.ps

C. Bordenave, Spectrum of random graphs
URL : https://hal.archives-ouvertes.fr/hal-00665907

C. Bordenave and P. Caputo, A large deviation principle for Wigner matrices without Gaussian tails, The Annals of Probability, vol.42, issue.6, pp.2454-2496, 2014.
DOI : 10.1214/13-AOP866

C. Bordenave and P. Caputo, Large deviations of empirical neighborhood distribution in sparse random graphs. Probab. Theory Related Fields, pp.149-222, 2015.

C. Bordenave, P. Caputo, and D. Chafaï, Spectrum of large random reversible Markov chains: Heavy-tailed weights on the complete graph, The Annals of Probability, vol.39, issue.4, pp.1544-1590, 2011.
DOI : 10.1214/10-AOP587

URL : https://hal.archives-ouvertes.fr/hal-00369621

C. Borell, Tail probabilities in Gauss space, Vector space measures and applications (Proc. Conf, pp.73-82, 1977.
DOI : 10.1016/0022-1236(73)90025-6

C. Borell, On polynomial chaos and integrability, Probab. Math. Statist, vol.3, issue.2, pp.191-203, 1984.

G. Borot and A. Guionnet, Asymptotic Expansion of ?? Matrix Models in the One-cut Regime, Communications in Mathematical Physics, vol.67, issue.4, pp.447-483, 2013.
DOI : 10.2307/1970008

M. Capitaine, C. Donati-martin, D. Féral, and M. Février, 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-00707371

R. Carmona and J. Lacroix, Spectral theory of random Schrödinger operators. Probability and its Applications, 1990.

D. Chafaï, A. Hardy, and M. Maïda, Concentration for Coulomb gases and Coulomb transport inequalities, Journal of Functional Analysis, vol.275, issue.6, 2016.
DOI : 10.1016/j.jfa.2018.06.004

S. Chatterjee and S. R. Varadhan, The large deviation principle for the Erd??s-R??nyi random graph, European Journal of Combinatorics, vol.32, issue.7, pp.1000-1017, 2011.
DOI : 10.1016/j.ejc.2011.03.014

URL : https://doi.org/10.1016/j.ejc.2011.03.014

S. Chatterjee and S. R. Varadhan, Large deviations for random matrices, Communications on Stochastic Analysis, vol.6, issue.1, pp.1-13, 2012.
DOI : 10.31390/cosa.6.1.02

F. Clarke, Functional analysis, calculus of variations and optimal control, Graduate Texts in Mathematics, vol.264
DOI : 10.1007/978-1-4471-4820-3

URL : https://hal.archives-ouvertes.fr/hal-00865914

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

J. Delon, J. Salomon, and A. Sobolevski, Local Matching Indicators for Transport Problems with Concave Costs, SIAM Journal on Discrete Mathematics, vol.26, issue.2, pp.801-827, 2012.
DOI : 10.1137/110823304

URL : https://hal.archives-ouvertes.fr/hal-00525994

A. Dembo and O. Zeitouni, Large deviations techniques and applications, volume 38 of Stochastic Modelling and Applied Probability, 1998.

R. Dobrushin, P. Groeneboom, and M. Ledoux, Lectures on probability theory and statistics Lectures from the 24th Saint-Flour Summer School held, Lecture Notes in Mathematics, vol.1648, 1994.

H. Döring and P. Eichelsbacher, Moderate Deviations in a Random Graph and for the Spectrum of Bernoulli Random Matrices, Electronic Journal of Probability, vol.14, issue.0, pp.2636-2656, 2009.
DOI : 10.1214/EJP.v14-723

I. Dumitriu and A. Edelman, Matrix models for beta ensembles, Journal of Mathematical Physics, vol.54, issue.2, pp.5830-5847, 2002.
DOI : 10.1063/1.531675

URL : http://arxiv.org/pdf/math-ph/0206043v1.pdf

F. J. Dyson, The Threefold Way. Algebraic Structure of Symmetry Groups and Ensembles in Quantum Mechanics, Journal of Mathematical Physics, vol.7, issue.6, pp.1199-1215, 1962.
DOI : 10.2307/1968599

D. E. Edmunds and H. Triebel, Function spaces, entropy numbers, differential operators, Cambridge Tracts in Mathematics, vol.120, 1996.
DOI : 10.1017/CBO9780511662201

P. Eichelsbacher and J. Sommerauer, Moderate deviations for traces of words in a mult-matrix model, Electronic Communications in Probability, vol.14, issue.0, pp.572-586, 2009.
DOI : 10.1214/ECP.v14-1515

Z. Füredi and J. Komlós, The eigenvalues of random symmetric matrices, Combinatorica, vol.67, issue.3, pp.233-241, 1981.
DOI : 10.1007/BF02579329

F. Gamboa, J. Nagel, and A. Rouault, Sum rules and large deviations for spectral measures on the unit circle, Random Matrices: Theory and Applications
DOI : 10.1016/j.jat.2005.02.003

URL : https://hal.archives-ouvertes.fr/hal-01300205

F. Gamboa, J. Nagel, and A. Rouault, Sum rules via large deviations, Journal of Functional Analysis, vol.270, issue.2, pp.509-559, 2016.
DOI : 10.1016/j.jfa.2015.08.009

URL : https://hal.archives-ouvertes.fr/hal-01168243

N. Gantert, K. Ramanan, and F. Rembart, Large deviations for weighted sums of stretched exponential random variables, Electronic Communications in Probability, vol.19, issue.0, 2014.
DOI : 10.1214/ECP.v19-3266

URL : http://doi.org/10.1214/ecp.v19-3266

N. Gozlan, Poincar?? inequalities and dimension free concentration of measure, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.46, issue.3, pp.708-739, 2010.
DOI : 10.1214/09-AIHP209

URL : http://doi.org/10.1214/09-aihp209

B. Groux, Asymptotic Freeness for Rectangular Random Matrices and Large Deviations for Sample Covariance Matrices With Sub-Gaussian Tails. arXiv

A. Guionnet, Large random matrices: lectures on macroscopic asymptotics, volume 1957 of Lecture Notes in Mathematics, Lectures from the 36th Probability Summer School held in Saint-Flour, 2006.

A. Guionnet and O. Zeitouni, Concentration of the Spectral Measure for Large Matrices, Electronic Communications in Probability, vol.5, issue.0, pp.119-136, 2000.
DOI : 10.1214/ECP.v5-1026

A. Guionnet and O. Zeitouni, Large Deviations Asymptotics for Spherical Integrals, Journal of Functional Analysis, vol.188, issue.2, pp.461-515, 2002.
DOI : 10.1006/jfan.2001.3833

A. Hardy, A note on large deviations for 2D Coulomb gas with weakly confining potential, Electronic Communications in Probability, vol.17, issue.0, 2012.
DOI : 10.1214/ECP.v17-1818

URL : https://hal.archives-ouvertes.fr/hal-01889789

J. B. Hough, M. Krishnapur, Y. Peres, and B. Virág, Zeros of Gaussian analytic functions and determinantal point processes, volume 51 of University Lecture Series, 2009.

K. Johansson, Shape Fluctuations and Random Matrices, Communications in Mathematical Physics, vol.209, issue.2, pp.437-476, 2000.
DOI : 10.1007/s002200050027

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

O. Kallenberg, Foundations of modern probability. Probability and its Applications, 1997.

R. Killip and I. Nenciu, Matrix models for circular ensembles, Int. Math. Res. Not, issue.50, pp.2665-2701, 2004.

A. Klein, Extended States in the Anderson Model on the Bethe Lattice, Advances in Mathematics, vol.133, issue.1, pp.163-184, 1998.
DOI : 10.1006/aima.1997.1688

R. Lata?-a and J. O. Wojtaszczyk, On the infimum convolution inequality, Studia Mathematica, vol.189, issue.2, pp.147-187, 2008.
DOI : 10.4064/sm189-2-5

M. R. Leadbetter, G. Lindgren, and H. Rootzén, Extremes and related properties of random sequences and processes, 1983.
DOI : 10.1007/978-1-4612-5449-2

T. Leblé and S. Serfaty, Large deviation principle for empirical fields of Log and Riesz gases, Inventiones mathematicae, vol.39, issue.28
DOI : 10.1088/0305-4470/39/28/S10

M. Ledoux, A note on large deviations for wiener chaos, Séminaire de Probabilités, XXIV, pp.1-14, 1988.
DOI : 10.2307/2371268

M. Ledoux, The concentration of measure phenomenon, volume 89 of Mathematical Surveys and Monographs, 2001.

M. Ledoux, A Remark on Hypercontractivity and Tail Inequalities for the Largest Eigenvalues of Random Matrices, Séminaire de Probabilités XXXVII, pp.360-369, 2003.
DOI : 10.1007/978-3-540-40004-2_14

M. Ledoux and B. Rider, Small Deviations for Beta Ensembles, Electronic Journal of Probability, vol.15, issue.0, pp.1319-1343, 2010.
DOI : 10.1214/EJP.v15-798

URL : https://hal.archives-ouvertes.fr/hal-00629692

M. Ledoux and M. Talagrand, Probability in Banach spaces, Mathematics and Related Areas, 1991.
DOI : 10.1007/978-3-642-20212-4

L. Lovász and B. Szegedy, Limits of dense graph sequences, Journal of Combinatorial Theory, Series B, vol.96, issue.6, pp.933-957, 2006.
DOI : 10.1016/j.jctb.2006.05.002

J. B. Martin, Limiting shape for directed percolation models, The Annals of Probability, vol.32, issue.4, pp.2908-2937, 2004.
DOI : 10.1214/009117904000000838

URL : http://doi.org/10.1214/009117904000000838

P. Massart, G. Lugosi, and S. Boucheron, Concentration Inequalities : A Nonasymptotic Theory of Independence, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00794821

B. Maurey, Some deviation inequalities, Geometric and Functional Analysis, vol.104, issue.2, pp.188-197, 1991.
DOI : 10.1007/BF01896377

URL : http://arxiv.org/pdf/math/9201216

M. Maïda, Large deviations for the largest eigenvalue of rank one deformations of Gaussian ensembles, Electronic Journal of Probability, vol.12, issue.0, pp.1131-1150, 2007.
DOI : 10.1214/EJP.v12-438

M. W. Meckes and S. J. Szarek, Concentration for noncommutative polynomials in random matrices, Proc. Amer, pp.1803-1813, 2012.
DOI : 10.1090/S0002-9939-2011-11262-0

URL : http://arxiv.org/pdf/1101.1923

S. V. Nagaev, Large Deviations of Sums of Independent Random Variables, The Annals of Probability, vol.7, issue.5, pp.745-789, 1979.
DOI : 10.1214/aop/1176994938

A. Pizzo, D. Renfrew, and A. Soshnikov, 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

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, pp.64-94, 2013.
DOI : 10.1214/11-AIHP459

URL : http://doi.org/10.1214/11-aihp459

J. A. Ramírez, B. Rider, and B. Virág, Beta ensembles, stochastic Airy spectrum, and a diffusion, Journal of the American Mathematical Society, vol.24, issue.4, pp.919-944, 2011.
DOI : 10.1090/S0894-0347-2011-00703-0

M. Reed and B. Simon, Methods of modern mathematical physics. I, 1980.

R. T. Rockafellar, Convex analysis. Princeton Landmarks in Mathematics, 1997.

S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional integrals and derivatives. Gordon and Breach Science Publishers, Theory and applications, 1993.

B. Simon, Orthogonal polynomials on the unit circle, 2005.
DOI : 10.1090/coll054.1

B. Simon, Equilibrium measures and capacities in spectral theory, Inverse Problems and Imaging, vol.1, issue.4, pp.713-772, 2007.
DOI : 10.3934/ipi.2007.1.713

URL : http://www.aimsciences.org/journals/doIpChk.jsp?paperID=2937&mode=full

Y. Sinai and A. Soshnikov, 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

Y. G. Sina?-i and A. Soshnikov, A refinement of Wigner's semicircle law in a neighborhood of the spectrum edge for random symmetric matrices, Functional Analysis and Its Applications, vol.75, issue.No. 1, pp.56-79, 1998.
DOI : 10.1007/BF01035768

R. Speicher, Free convolution and the random sum of matrices, Publications of the Research Institute for Mathematical Sciences, vol.29, issue.5, pp.731-744, 1993.
DOI : 10.2977/prims/1195166573

URL : http://www.ems-ph.org/journals/show_pdf.php?issn=0034-5318&vol=29&iss=5&rank=1

R. P. Stanley, With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin, 1999.

M. Talagrand, A new isoperimetric inequality and the concentration of measure phenomenon, Lecture Notes in Math, vol.68, pp.94-124, 1989.
DOI : 10.1007/BF00535169

M. Talagrand, The Supremum of Some Canonical Processes, American Journal of Mathematics, vol.116, issue.2, pp.283-325, 1994.
DOI : 10.2307/2374931

M. Talagrand, Transportation cost for Gaussian and other product measures, Geometric and Functional Analysis, vol.27, issue.3, pp.587-600, 1996.
DOI : 10.1007/BF02699376

R. C. Thompson, Convex and concave functions of singular values of matrix sums, Pacific Journal of Mathematics, vol.66, issue.1, pp.285-290, 1976.
DOI : 10.2140/pjm.1976.66.285

C. A. Tracy and H. Widom, Level-spacing distributions and the Airy kernel, Communications in Mathematical Physics, vol.21, issue.1, pp.151-174, 1994.
DOI : 10.1002/j.1538-7305.1961.tb03976.x

C. Villani, Topics in optimal transportation, Graduate Studies in Mathematics, vol.58, 2003.
DOI : 10.1090/gsm/058

C. Villani, Optimal transport, of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 2009.
DOI : 10.1007/978-3-540-71050-9

URL : https://hal.archives-ouvertes.fr/hal-00923320

B. Virág, Operator limits of random matrices, Proceedings of the International Congress of Mathematicians, p.2014

J. , V. Neumann, and E. Wigner, Uber das Verhalten von Eigenwerten bei adiabatischen Prozesses, Phys. Z, vol.30, pp.467-470, 1929.

V. H. Vu, Spectral norm of random matrices, Combinatorica, vol.207, issue.3, pp.721-736, 2007.
DOI : 10.1007/s00493-007-2190-z

E. P. Wigner, On the Distribution of the Roots of Certain Symmetric Matrices, The Annals of Mathematics, vol.67, issue.2, pp.325-327, 1958.
DOI : 10.2307/1970008

X. Zhan, Matrix inequalities, volume 1790 of Lecture Notes in Mathematics, 2002.