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

M. Anshelevich and A. N. Sengupta, Quantum free Yang???Mills on the plane, Journal of Geometry and Physics, vol.62, issue.2, pp.330-343, 2012.
DOI : 10.1016/j.geomphys.2011.10.005

F. Thomas, W. F. Banchoff, and . Pohl, A generalization of the isoperimetric inequality, J. Differential Geometry, vol.6, pp.175-19272, 1971.

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

P. Biane, Free Brownian motion, free stochastic calculus, and random matrices, Free probability theory, pp.1-19, 1995.
DOI : 10.1090/fic/012/01

P. Biane, Segal???Bargmann Transform, Functional Calculus on Matrix Spaces and the Theory of Semi-circular and Circular Systems, Journal of Functional Analysis, vol.144, issue.1, pp.232-286, 1997.
DOI : 10.1006/jfan.1996.2990

J. S. Birman, Braids, Links and Mapping Class Group, Annals of Mathematics Studies, 1975.

D. Bump, Lie groups. Graduate texts in mathematics, 2004.

E. Cépa and D. Lépingle, Brownian particles with electrostatic repulsion on the circle: Dyson's model for unitary random matrices revisited, ESAIM: Probability and Statistics, vol.5, pp.203-224, 2001.
DOI : 10.1051/ps:2001109

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, J. A. Mingo, P. ?niady, 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 M. Stolz, 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 S. Matsumoto, On some properties of orthogonal Weingarten functions, Journal of Mathematical Physics, vol.50, issue.11, p.113516, 2009.
DOI : 10.1063/1.3251304

B. Collins and P. ?niady, 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

D. Anthony, P. Aristotile, C. M. Diaconis, and . Newman, Brownian motion and the classical groups, Probability, statistics and their applications, pp.97-116, 2003.

C. De, C. , and C. Procesi, A characteristic free approach to invariant theory, Advances in Math, vol.21, issue.3, pp.330-354, 1976.

S. Bart-de, The fundamental group of the hawaiian earring is not free, International Journal of Algebra and Computation, vol.2, issue.12, pp.33-37, 1992.

P. Diaconis and S. N. 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, Journal of Applied Probability, vol.31, issue.3, pp.49-62, 1994.
DOI : 10.2307/3214948

K. Bruce and . Driver, YM 2 : Continuum expectations, lattice convergence, and lassos, Commun. Math. Phys, vol.123, issue.4, pp.575-616, 1989.

L. Erd?s, B. Schlein, and H. Yau, Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices. ArXiv e-prints, 2007.

F. Gabriel, Planar markovian holonomy fields : construction, characterization and application

D. J. Gross, Two-dimensional QCD as a string theory, Nuclear Physics B, vol.400, issue.1-3, pp.161-180, 1993.
DOI : 10.1016/0550-3213(93)90402-B

J. David, A. Gross, and . Matytsin, Some properties of large-n two-dimensional yang-mills theory, Nuclear Physics B, vol.437, issue.3, pp.541-584, 1995.

J. David, A. Gross, and . Matytsin, Some properties of large-N two-dimensional Yang- Mills theory, Nuclear Phys. B, vol.437, issue.3, pp.541-584, 1995.

T. Halverson and A. Ram, Partition algebras, European Journal of Combinatorics, vol.26, issue.6, pp.869-921, 2005.
DOI : 10.1016/j.ejc.2004.06.005

B. Hambly and T. Lyons, Uniqueness for the signature of a path of bounded variation and the reduced path group, Annals of Mathematics, vol.171, issue.1, pp.109-167, 2010.
DOI : 10.4007/annals.2010.171.109

P. Stephen and . Humphries, On weakly distinguished bases and free generating sets of free groups, The Quarterly Journal of Mathematics, vol.36, issue.2, pp.215-219, 1985.

V. F. Jones, The Potts model and the symmetric group, In Subfactors (Kyuzeso World Sci. Publ, pp.259-267, 1993.

A. Adolfas and J. , Symmetric polynomials and the center of the symmetric group ring, Rep. Mathematical Phys, vol.5, issue.1, pp.107-112, 1974.

V. A. Kazakov, Wilson loop average for an arbitrary contour in two-dimensional U(N) gauge theory, Nuclear Physics B, vol.179, issue.2, pp.283-292, 1981.
DOI : 10.1016/0550-3213(81)90239-X

V. A. Kazakov and I. K. Kostov, Computation of the Wilson loop functional in two-dimensional U(???) lattice gauge theory, Physics Letters B, vol.105, issue.6, pp.453-456, 1981.
DOI : 10.1016/0370-2693(81)91203-X

T. Lévy, Schur???Weyl duality and the heat kernel measure on the unitary group, Advances in Mathematics, vol.218, issue.2, pp.537-575, 2008.
DOI : 10.1016/j.aim.2008.01.006

T. Lévy, The master field on the plane. ArXiv e-prints, 2011.

T. Lévy and M. Maïda, 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

T. Lévy, Wilson loops in the light of spin networks, Journal of Geometry and Physics, vol.52, issue.4, pp.382-397, 2004.
DOI : 10.1016/j.geomphys.2004.04.003

T. Lévy, Two-dimensional Markovian holonomy fields, 2010.

I. G. Macdonald, Lévy Processes in Lie Groups

I. G. Macdonald, Symmetric functions and Hall polynomials, Cambridge Tracts in Mathematics

Y. M. Makeenko and A. A. , Exact equation for the loop average in multicolor QCD, Physics Letters B, vol.88, issue.1-2, pp.135-137, 1979.
DOI : 10.1016/0370-2693(79)90131-X

P. Méliot, The cut-off phenomenon for Brownian motions on symmetric spaces of compact type. ArXiv e-prints, 2012.

J. Milnor, Curvatures of left invariant metrics on lie groups, Advances in Mathematics, vol.21, issue.3, pp.293-329, 1976.
DOI : 10.1016/S0001-8708(76)80002-3

J. A. Mingo, P. ?niady, 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. James, R. Mingo, and . Speicher, Second order freeness and fluctuations of random matrices. I. Gaussian and Wishart matrices and cyclic Fock spaces, J. Funct. Anal, vol.235, issue.1, pp.226-270, 2006.

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

A. Okounkov and A. Vershik, A new approach to representation theory of symmetric groups, Selecta Mathematica, vol.38, issue.no. 4, pp.581-605, 1996.
DOI : 10.1007/BF02433451

C. and E. I. Redelmeier, Real Second-Order Freeness and Fluctuations of Random Matrices, Thesis (Ph.D.)?Queen's University (Canada)

A. Sengupta, Gauge invariant functions of connections, Proceedings of the American Mathematical Society, vol.121, issue.3, pp.897-905, 1994.
DOI : 10.1090/S0002-9939-1994-1215205-7

A. Sengupta, Gauge theory on compact surfaces, Memoirs of the American Mathematical Society, vol.126, issue.600, p.85, 1997.
DOI : 10.1090/memo/0600

G. Hooft, A planar diagram theory for strong interactions, Nuclear Physics B, vol.72, issue.3, pp.461-473, 1974.
DOI : 10.1016/0550-3213(74)90154-0

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

D. Weingarten, Asymptotic behavior of group integrals in the limit of infinite rank, Journal of Mathematical Physics, vol.19, issue.5, pp.999-1001, 1978.
DOI : 10.1063/1.523807

F. Xu, A Random Matrix Model From Two Dimensional Yang-Mills Theory, Communications in Mathematical Physics, vol.190, issue.2, pp.287-307, 1997.
DOI : 10.1007/s002200050242

P. Zinn-justin, Jucys???Murphy Elements and Weingarten Matrices, Letters in Mathematical Physics, vol.19, issue.5, pp.119-127, 2010.
DOI : 10.1007/s11005-009-0365-9