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

F. Bekerman, Transport maps for ?-matrix models in the multi-cut matrix regime, 2015.

F. Bekerman, A. Figalli, and A. Guionnet, Transport Maps for $${\beta}$$ ?? -Matrix Models and Universality, Communications in Mathematical Physics, vol.55, issue.1???2, pp.589-619, 2015.
DOI : 10.1007/s00220-015-2384-y

P. Biane and R. Speicher, Stochastic calculus with respect to free Brownian motion and analysis on Wigner space. Probab. Theory Related Fields, pp.373-409, 1998.

P. Biane and R. Speicher, Free diffusions, free entropy and????free????Fisher????information, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.37, issue.5, pp.581-606, 2001.
DOI : 10.1016/S0246-0203(00)01074-8

A. Borodin, V. Gorin, and A. Guionnet, Gaussian asymptotics of discrete ?? $\beta $ -ensembles, Publications math??matiques de l'IH??S, vol.67, 1505.
DOI : 10.1007/s10240-016-0085-5

URL : https://hal.archives-ouvertes.fr/ensl-01400956

G. Borot and B. Eynard, All-order asymptotics of hyperbolic knot invariants from nonperturbative topological recursion of A-polynomials

G. Borot and A. Guionnet, Asymptotic Expansion of ? Matrix Models in the multi-cut Regime, 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

G. Borot, A. Guionnet, and K. Kozlowski, Large-n asymptotic expansion for mean field models with coulomb gas interaction, Int. Math. Res. Not, 2015.

P. Bourgade, L. Erdös, and H. Yau, Edge Universality of Beta Ensembles, Communications in Mathematical Physics, vol.94, issue.3???4, pp.261-353, 2014.
DOI : 10.1007/s00220-014-2120-z

P. Bourgade, L. Erdhos, and H. Yau, Universality of general $\beta$ -ensembles, Duke Mathematical Journal, vol.163, issue.6, pp.1127-1190, 2014.
DOI : 10.1215/00127094-2649752

L. Chekhov and B. Eynard, Matrix eigenvalue model: Feynman graph technique for all genera, Journal of High Energy Physics, vol.39, issue.12, 2006.
DOI : 10.1007/s11005-005-0157-9

URL : https://hal.archives-ouvertes.fr/hal-00022361

B. Collins, Moments and cumulants of polynomial random variables on unitary groups, the Itzykson-Zuber integral, and free probability, Int. Math. Res. Not, issue.17, pp.953-982, 2003.

B. Collins, A. Guionnet, and E. Maurel-segala, Asymptotics of unitary and orthogonal matrix integrals, Advances in Mathematics, vol.222, issue.1, pp.172-215, 2009.
DOI : 10.1016/j.aim.2009.03.019

Y. Dabrowski, A note about proving non-?? under a finite non-microstates free Fisher information assumption, Journal of Functional Analysis, vol.258, issue.11, pp.3662-3674, 2010.
DOI : 10.1016/j.jfa.2010.02.010

Y. Dabrowski, Analytic functions relative to a covariance map ?: I. generalized haagerup products and analytic relations, 1503.

Y. Dabrowski, A. Guionnet, and D. Shlyakhtenko, Free transport for convex potentials, 2016.

Y. Dabrowski and A. Ioana, Unbounded derivations, free dilations, and indecomposability results for II$_1$ factors, Transactions of the American Mathematical Society, vol.368, issue.7, pp.4525-4560, 2016.
DOI : 10.1090/tran/6470

URL : https://hal.archives-ouvertes.fr/hal-00868672

P. Deift and D. Gioev, Random matrix theory: invariant ensembles and universality, Courant Lecture Notes in Mathematics. Courant Institute of Mathematical Sciences, vol.18, 2009.
DOI : 10.1090/cln/018

B. Eynard and N. Orantin, Invariants of algebraic curves and topological expansion, Communications in Number Theory and Physics, vol.1, issue.2, pp.347-452, 2007.
DOI : 10.4310/CNTP.2007.v1.n2.a4

URL : https://hal.archives-ouvertes.fr/hal-00130963

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, V. F. Jones, and D. Shlyakhtenko, Random matrices, free probability, planar algebras and subfactors, Quanta of maths, pp.201-239, 2010.

A. Guionnet, V. F. Jones, D. Shlyakhtenko, and P. Zinn-justin, Loop Models, Random Matrices and Planar Algebras, Communications in Mathematical Physics, vol.6, issue.3, pp.45-97, 2012.
DOI : 10.1007/s00220-012-1573-1

A. Guionnet and E. Maurel-segala, Combinatorial aspects of matrix models, ALEA Lat. Am. J. Probab. Math. Stat, vol.1, pp.241-279, 2006.

A. Guionnet and E. Maurel-segala, 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

A. Guionnet and J. Novak, Asymptotics of unitary multimatrix models: The Schwinger???Dyson lattice and topological recursion, Journal of Functional Analysis, vol.268, issue.10, 2014.
DOI : 10.1016/j.jfa.2015.03.002

A. Guionnet and D. Shlyakhtenko, Free Diffusions and Matrix Models with Strictly Convex Interaction, Geometric and Functional Analysis, vol.18, issue.6, pp.1875-1916, 2009.
DOI : 10.1007/s00039-009-0704-0

A. Guionnet and D. Shlyakhtenko, Free monotone transport, Inventiones mathematicae, vol.34, issue.3, pp.613-661, 2014.
DOI : 10.1007/s00222-013-0493-9

U. Haagerup and S. Thorbjørnsen, )) is not a group, Annals of Mathematics, vol.162, issue.2, pp.711-775, 2005.
DOI : 10.4007/annals.2005.162.711

V. Jones, D. Shlyakhtenko, and K. Walker, An orthogonal approach to the subfactor of a planar algebra, Pacific Journal of Mathematics, vol.246, issue.1, pp.187-197, 2010.
DOI : 10.2140/pjm.2010.246.187

N. Nekrasov, Non-perturbative dyson?schwinger equations and bps/cft correspondence. in preparation, 2015.

N. Nekrasov and V. Pestun, Seiberg-witten geometry of four dimensional n = 2 quiver gauge theories, 2012.

N. Nekrasov, V. Pestun, and S. Shatashvili, Quantum geometry and quiver gauge theories. High Energy Physics -Theory, pp.1-83, 2013.

]. B. Nelson, Free Monotone Transport Without a Trace, Communications in Mathematical Physics, vol.132, issue.3, 2013.
DOI : 10.1007/s00220-014-2148-0

B. Nelson, Free transport for finite depth subfactor planar algebras, Journal of Functional Analysis, vol.268, issue.9, 1406.
DOI : 10.1016/j.jfa.2014.12.018

N. Ozawa, There is no separable universal II 1 -factor, Proceedings of the American Mathematical Society, vol.132, issue.02, pp.487-490, 2004.
DOI : 10.1090/S0002-9939-03-07127-2

L. Pastur, Limiting laws of linear eigenvalue statistics for Hermitian matrix models, Journal of Mathematical Physics, vol.47, issue.10, p.103303, 2006.
DOI : 10.1063/1.2356796

J. Ramirez, B. Rider, and B. Virag, 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. Shcherbina, Change of variables as a method to study general beta-models: bulk universality, 2013.

T. Tao, The asymptotic distribution of a single eigenvalue gap of a Wigner matrix, Probability Theory and Related Fields, vol.177, issue.1, pp.81-106, 2013.
DOI : 10.1007/s00440-012-0450-3

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 : 10.1007/BF02100489

C. A. Tracy and H. Widom, Level spacing distributions and the Bessel kernel, Communications in Mathematical Physics, vol.13, issue.2, pp.289-309, 1994.
DOI : 10.1007/BF02099779

F. G. Tricomi, Integral equations, Pure and Applied Mathematics, 1957.

W. T. Tutte, A census of planar maps. Canad, J. Math, vol.15, pp.249-271, 1963.

D. Voiculescu, The coalgebra of the free difference quotient and free probability, Internat. Math. Res. Notices, issue.2, pp.79-106, 2000.

D. Voiculescu, A note on cyclic gradients, Indiana University Mathematics Journal, vol.49, issue.3, pp.837-841, 2000.
DOI : 10.1512/iumj.2000.49.2077

D. Voiculescu, Aspects of free analysis, Japanese Journal of Mathematics, vol.2004, issue.2, pp.163-183, 2008.
DOI : 10.1007/s11537-008-0753-4

A. Zvonkin, Matrix integrals and map enumeration: An accessible introduction, Mathematical and Computer Modelling, vol.26, issue.8-10, pp.8-10281, 1995.
DOI : 10.1016/S0895-7177(97)00210-0