S. Albeverio, L. Pastur, and M. Shcherbina, On the 1/n Expansion for Some Unitary Invariant Ensembles of Random Matrices, Communications in Mathematical Physics, vol.224, issue.1, pp.271-305, 2001.
DOI : 10.1007/s002200100531

G. Anderson, A. Guionnet, and O. Zeitouni, An introduction to random matrices, 2010.
DOI : 10.1017/CBO9780511801334

A. Auffinger, G. B. Arous, and J. And?ern-`-yand?and?ern-`-and?ern-`-y, Random Matrices and Complexity of Spin Glasses, Communications on Pure and Applied Mathematics, vol.134, issue.3, pp.165-201, 2013.
DOI : 10.1002/cpa.21422

P. Baldi, Large deviations and stochastic homogenization, Annali di Matematica Pura ed Applicata, vol.2, issue.1, pp.161-177, 1988.
DOI : 10.1007/BF01762793

B. Arous, G. Dembo, A. Guionnet, and A. , Aging of spherical spin glasses, Probability Theory and Related Fields, vol.120, issue.1, pp.1-67, 2001.
DOI : 10.1007/PL00008774

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

G. Borot and A. Guionnet, Asymptotic expansion of ? matrix models in the multi-cut regime. arXiv preprint, 2013.

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 : 10.1007/s00220-012-1619-4

P. Bourgade, A. Nikeghbali, and A. Rouault, Circular Jacobi Ensembles and Deformed Verblunsky Coefficients, International Mathematics Research Notices, issue.23, pp.4357-4394, 2009.
DOI : 10.1093/imrn/rnp092
URL : https://hal.archives-ouvertes.fr/hal-00672881

D. Damanik, R. Killip, and B. Simon, Perturbations of orthogonal polynomials with periodic recursion coefficients, Annals of Mathematics, vol.171, issue.3, pp.1931-2010, 2010.
DOI : 10.4007/annals.2010.171.1931

P. Deift, T. Kriecherbauer, K. Mclaughlin, S. Venakides, and X. Zhou, Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory, Communications on Pure and Applied Mathematics, vol.20, issue.2, pp.521335-1425, 1999.
DOI : 10.1002/(SICI)1097-0312(199911)52:11<1335::AID-CPA1>3.0.CO;2-1

H. Dette and W. Studden, The theory of canonical moments with applications in statistics , probability, and analysis, 1997.

I. Dumitriu and A. Edelman, Matrix models for beta ensembles, Journal of Mathematical Physics, vol.43, issue.11, pp.5830-5847, 2002.
DOI : 10.1063/1.1507823

C. Fan, A. Guionnet, Y. Song, and A. Wang, Convergence of eigenvalues to the support of the limiting measure in critical ? matrix models. arXiv preprint, 2014.

F. Gamboa and L. Lozada-chang, Large deviations for random power moment problem . The Annals of Probability, pp.2819-2837, 2004.

F. Gamboa, J. Nagel, A. Rouault, and J. Wagener, Large deviations for random matricial moment problems, Journal of Multivariate Analysis, vol.106, pp.17-35, 2012.
DOI : 10.1016/j.jmva.2011.11.006
URL : https://hal.archives-ouvertes.fr/hal-00531668

F. Gamboa and A. Rouault, Canonical Moments and Random Spectral Measures, Journal of Theoretical Probability, vol.208, issue.1, pp.1015-1038, 2010.
DOI : 10.1007/s10959-009-0239-1
URL : https://hal.archives-ouvertes.fr/hal-00226508

F. Gamboa and A. Rouault, Large Deviations for Random Spectral Measures and Sum Rules, Applied Mathematics Research eXpress, vol.2011, issue.2, pp.281-307, 2011.
DOI : 10.1093/amrx/abr009
URL : https://hal.archives-ouvertes.fr/hal-00276017

A. Hardy, A note on large deviations for 2D Coulomb gas with weakly confining potential, Electronic Communications in Probability, vol.17, issue.0, pp.171-183, 2012.
DOI : 10.1214/ECP.v17-1818

K. Johansson, On fluctuations of eigenvalues of random Hermitian matrices, Duke Mathematical Journal, vol.91, issue.1, pp.151-204, 1998.
DOI : 10.1215/S0012-7094-98-09108-6

R. Killip, Spectral theory via sum rules In Spectral theory and mathematical physics: a Festschrift in honor of Barry Simon's 60th birthday, Proc. Sympos. Pure Math, vol.76, pp.907-930, 2007.

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

R. Killip and B. Simon, Sum rules for Jacobi matrices and their applications to spectral theory, Annals of Mathematics, vol.158, issue.1, pp.253-321, 2003.
DOI : 10.4007/annals.2003.158.253

M. Krishnapur, B. Rider, and B. Virag, Universality of the Stochastic Airy Operator, Communications on Pure and Applied Mathematics, vol.34, issue.1, 2013.
DOI : 10.1002/cpa.21573

S. Kupin, Spectral properties of Jacobi matrices and sum rules of special form, Journal of Functional Analysis, vol.227, issue.1, pp.1-29, 2005.
DOI : 10.1016/j.jfa.2005.04.016

F. Nazarov, F. Peherstorfer, A. Volberg, Y. , and P. , On generalized sum rules for Jacobi matrices, Int. Math. Res. Not, issue.3, pp.155-186, 2005.

R. Rockafellar, Integrals which are convex functionals. II, Pacific Journal of Mathematics, vol.39, issue.2, pp.439-469, 1971.
DOI : 10.2140/pjm.1971.39.439
URL : http://projecteuclid.org/download/pdf_1/euclid.pjm/1102986512

N. Saitoh and H. Yoshida, The infinite divisibility and orthogonal polynomials with a constant recursion formula in free probability theory, Probab. Math. Statist. Acta Univ. Wratislav, vol.21, issue.1 2298, pp.159-170, 2001.

S. Serfaty, Coulomb gases and Ginzburg-Landau vortices, 2014.
DOI : 10.4171/152
URL : https://hal.archives-ouvertes.fr/hal-01377803

B. Simon, Orthogonal polynomials with exponentially decaying recursion coefficients, Probability and mathematical physics, pp.453-463, 2007.

B. Simon, Szeg? o's theorem and its descendants. M. B. Porter Lectures, 2011.
DOI : 10.1515/9781400837052

H. Trotter, Eigenvalue distributions of large Hermitian matrices; Wigner's semi-circle law and a theorem of Kac, Murdock, and Szeg??, Advances in Mathematics, vol.54, issue.1, pp.67-82, 1984.
DOI : 10.1016/0001-8708(84)90037-9

N. Xia, Y. Qin, and Z. Bai, Convergence rates of eigenvector empirical spectral distribution of large dimensional sample covariance matrix, The Annals of Statistics, vol.41, issue.5, pp.2572-2607, 2013.
DOI : 10.1214/13-AOS1154