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A. Borodin, P. L. Ferrari, M. Praehofer, and T. Sasamoto, Fluctuation Properties of the TASEP with??Periodic??Initial??Configuration, Journal of Statistical Physics, vol.177, issue.5-6, pp.1055-1080, 2007.
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E. Brezin and S. Hikami, Intersection numbers from the antisymmetric Gaussian matrix model, Journal of High Energy Physics, vol.2008, issue.07
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M. Caselle and U. Magnea, Random matrix theory and symmetric spaces, Physics Reports, vol.394, issue.2-3, pp.41-156, 2004.
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B. Collins and P. Sniady, Representation of Lie groups and random matrices, arXiv : math/0610285, to appear in Trans

M. Defosseux, Orbit measures and interlaced determinantal point processes, arXiv :0802.4183, to appear in C, R. Acad. Sci. Paris, Ser. I, vol.346, 2008.
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P. Diaconis and M. Shahshahani, The Subgroup Algorithm for Generating Uniform Random Variables, Probability in the Engineering and Informational Sciences, vol.1, issue.01, pp.15-32, 1987.
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A. H. Dooley, J. Repka, and N. J. Wildberger, Sums of adjoint orbits, Linear and Multilinear Algebra, pp.79-101, 1993.

A. H. Dooley and N. J. Wildberger, Harmonic analysis and the global exponential map for compact Lie groups, Functional Analysis and Its Applications, vol.29, issue.3, pp.25-32, 1993.
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P. Eichelsbacher and M. Stolz, Large deviations for random matrix ensembles in mesoscopic physics

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P. J. Forrester and E. Nordenstam, The anti?symmetric GUE minor process, arXiv :math?pr/0804

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I. M. Gelfand and M. L. Tsetlin, Finite dimensional representations of the group of unimodular matrices, Dokl. Akad. Nauk. USSR, vol.71, pp.275-290, 1981.

F. Gillet, Asymptotic behaviour of watermelons, 2003.

N. R. Goodman, Statistical Analysis Based on a Certain Multivariate Complex Gaussian Distribution (An Introduction), The Annals of Mathematical Statistics, vol.34, issue.1, pp.152-177, 1963.
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G. J. Heckman, Projections of orbits and asymptotic behavior of multiplicities for compact connected Lie groups, Inventiones Mathematicae, vol.6, issue.No 8, pp.333-356, 1982.
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P. Heinzner, A. Huckleberry, and M. R. Zirnbauer, Symmetry Classes of Disordered Fermions, Communications in Mathematical Physics, vol.37, issue.3, pp.725-771, 2005.
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K. Johansson, Random matrices and determinantal processes, arXiv :math? ph, 5100381.
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K. Johansson and E. Nordenstam, Eigenvalues of GUE Minors, Electronic Journal of Probability, vol.11, issue.0, pp.1342-1371, 2006.
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M. Kashiwara, On crystal bases, Representations of Groups, CMS Conference proceedings, Amer. Math. Soc, vol.16, pp.155-197, 1995.

M. Kashiwara and T. Nakashima, Crystal Graphs for Representations of the q-Analogue of Classical Lie Algebras, Journal of Algebra, vol.165, issue.2, pp.295-345, 1994.
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M. Katori, H. Tanemura, T. Nagao, and N. Komatsuda, Vicious walks with a wall, noncolliding meanders, and chiral and Bogoliubov???de Gennes random matrices, Physical Review E, vol.68, issue.2, pp.21112-21113, 2003.
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M. Katori and H. Tanemura, Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems, Journal of Mathematical Physics, vol.45, issue.8, pp.3058-3085, 2004.
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M. Katori and H. Tanemura, Nonintersecting paths, Noncolliding diffusion processes and representation theory, RIMS Kokyuroku, pp.1438-83, 2005.
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A. A. Kirillov, Merits and demerits of the orbit method, Bulletin of the American Mathematical Society, vol.36, issue.04, pp.433-488, 1999.
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A. A. Kirillov, Lectures on the orbit method, Graduate Studies in Mathematics, vol.64, 2004.
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A. Klyachko, Random walks on symmetric spaces and inequalities for matrix spectra, Linear Algebra and its Applications, vol.319, issue.1-3, pp.37-59, 2000.
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A. W. Knapp, Lie groups, beyond an introduction, 2002.
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C. Krattenthaler, A. J. Guttmann, and X. G. Viennot, Vicious walkers, friendly walkers and Young tableaux: II. With a wall, Journal of Physics A: Mathematical and General, vol.33, issue.48, pp.33-48, 2000.
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M. L. Mehta and N. Rosenzweig, Distribution laws for the roots of a random antisymmetric hermitian matrix, Nuclear Physics A, vol.109, issue.2, pp.449-456, 1968.
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T. Nakashima, Crystal base and a generalization of the Littlewood-Richardson rule for the classical Lie algebras, Communications in Mathematical Physics, vol.88, issue.2, pp.215-243, 1993.
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A. Okounkov and N. Reshetikhin, The birth of random matrix, Moscow Mathematical Journal, vol.6, pp.553-566, 2006.

A. Okounkov, Random matrices and random permutations, Internat. Math. Res. Notices no, vol.20, pp.1043-1095, 2000.

G. Olshanski, Unitary representations of (G,K)-pairs that are connected with the infinite symmetric group S(?), Leningrad Math, J, vol.1, pp.983-1014, 1990.

G. Olshanski, Unitary representation of infinite dimensional pairs (G,K) and the formalism of R.Howe. Representation of Lie groups and related topics, Advanced Studies in Contemporary Mathematics, 1990.

G. Olshanski, The problem of harmonic analysis on the infinite-dimensional unitary group, Journal of Functional Analysis, vol.205, issue.2, pp.464-524, 2003.
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G. Olshanski and A. Vershik, Ergodic unitary invariant measures on the space of infinite Hermitian matrices, Amer. Math. soc. Translations, vol.2, pp.175-137, 1996.

U. Porod, The cut-off phenomenon for random reflections, The Annals of Probability, vol.24, issue.1, pp.74-96, 1996.
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U. Porod, The out-off phenomenon for random reflections II: Complex and quaternionic cases, Probability Theory and Related Fields, vol.217, issue.2, pp.181-209, 1996.
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. Rosenthal, Random Rotations: Characters and Random Walks on SO(N), The Annals of Probability, vol.22, issue.1, pp.398-423, 1994.
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URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.54.2047

M. Roesler, Bessel convolutions on matrix cones, Compositio Mathematica, vol.143, issue.03, pp.749-779, 2007.
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J. J. Verbaarschot, Spectrum of the QCD Dirac operator and chiral random matrix theory, Physical Review Letters, vol.72, issue.16, pp.72-2531, 1994.
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D. Wang, Spiked models in Wishart Ensemble

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E. P. Wigner, On the statistical distribution of the widths and spacings of nuclear resonance levels, Proc. Cambridge Philos. Soc, pp.47-790, 1951.
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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.
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J. Wishart, THE GENERALISED PRODUCT MOMENT DISTRIBUTION IN SAMPLES FROM A NORMAL MULTIVARIATE POPULATION, Biometrika, vol.20, issue.1-2, pp.20-32, 1928.
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D. P. Zhelobenko, Compact Lie groups and their representations, Transl. of Math. Monographs, vol.40, 1973.

A. Altland and M. Zirnbauer, Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures, Physical Review B, vol.55, issue.2, pp.1142-1161, 1997.
DOI : 10.1103/PhysRevB.55.1142

Y. Baryshnikov, GUEs and queues, Probab. Theory Relat, pp.256-274, 2001.
DOI : 10.1007/pl00008760

A. Berenstein and A. Zelevinsky, Tensor product multiplicities and convex polytopes in partition space, Journal of Geometry and Physics, vol.5, issue.3, pp.453-472, 1989.
DOI : 10.1016/0393-0440(88)90033-2

E. Borel, Sur les principes de la th??orie cin??tique des gaz, Annales scientifiques de l'??cole normale sup??rieure, vol.23, pp.9-32, 1906.
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A. Borodin and G. Olshanski, Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes, Annals of Mathematics, vol.161, issue.3, pp.1319-1422, 2005.
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A. Borodin, P. L. Ferrari, M. Praehofer, and T. Sasamoto, Fluctuation Properties of the TASEP with??Periodic??Initial??Configuration, Journal of Statistical Physics, vol.177, issue.5-6, pp.1055-1080, 2007.
DOI : 10.1007/s10955-007-9383-0

E. Brezin, S. Hikami, and A. I. Larkin, Level statistics inside the vortex of a superconductor and symplectic random-matrix theory in an external source, Physical Review B, vol.60, issue.5, pp.60-3589, 1999.
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URL : https://hal.archives-ouvertes.fr/hal-00005190

E. Brezin and S. Hikami, Intersection numbers from the antisymmetric Gaussian matrix model, Journal of High Energy Physics, vol.2008, issue.07
DOI : 10.1088/1126-6708/2008/07/050

URL : https://hal.archives-ouvertes.fr/hal-00286913

M. F. Bru and W. Process, Wishart processes, Journal of Theoretical Probability, vol.20, issue.4, pp.725-751, 1991.
DOI : 10.1007/BF01259552

J. Cardy, Network Models in Class C on Arbitrary Graphs, Communications in Mathematical Physics, vol.37, issue.1, pp.11-87, 2005.
DOI : 10.1007/s00220-005-1304-y

M. Caselle and U. Magnea, Random matrix theory and symmetric spaces, Physics Reports, vol.394, issue.2-3, pp.41-156, 2004.
DOI : 10.1016/j.physrep.2003.12.004

URL : http://arxiv.org/abs/cond-mat/0304363

H. Cohn, M. Larsen, and J. Propp, The shape of a typical boxed plane partition, New York J. Math, vol.4, p.137165, 1998.

B. Collins and P. Sniady, Representation of Lie groups and random matrices, arXiv: math/0610285, to appear in Trans

M. Defosseux, Orbit measures and interlaced determinantal point processes, Comptes Rendus Mathematique, vol.346, issue.13-14, pp.783-788, 2008.
DOI : 10.1016/j.crma.2008.05.016

URL : https://hal.archives-ouvertes.fr/hal-00315365

P. Diaconis, Products of random matrices as they arise in the study of random walks on groups, Contemp. Math, vol.50, pp.183-195, 1986.
DOI : 10.1090/conm/050/841092

P. Diaconis and M. Shahshahani, The Subgroup Algorithm for Generating Uniform Random Variables, Probability in the Engineering and Informational Sciences, vol.1, issue.01, pp.15-32, 1987.
DOI : 10.2307/2045709

A. H. Dooley, J. Repka, and N. J. Wildberger, Sums of adjoint orbits, Linear and Multilinear Algebra, pp.79-101, 1993.

A. H. Dooley and N. J. Wildberger, Harmonic analysis and the global exponential map for compact Lie groups, Functional Analysis and Its Applications, vol.29, issue.3, pp.25-32, 1993.
DOI : 10.1007/BF01768664

F. J. Dyson, The Threefold Way. Algebraic Structure of Symmetry Groups and Ensembles in Quantum Mechanics, Journal of Mathematical Physics, vol.3, issue.6, pp.1199-1215, 1962.
DOI : 10.1063/1.1703863

P. Eichelsbacher and M. Stolz, Large deviations for random matrix ensembles in mesoscopic physics

J. Faraut, Infinite dimensional spherical analysis. COE Lecture Note DMHF, 2008.

P. J. Forrester, Log?gases and Random matrices
DOI : 10.1515/9781400835416

P. J. Forrester and E. Nordenstam, The anti?symmetric GUE minor process, arXiv:math? pr/0804

M. Fulmek and C. Krattenthaler, Lattice Path Proofs for Determinantal Formulas for Symplectic and Orthogonal Characters, Journal of Combinatorial Theory, Series A, vol.77, issue.1, pp.3-50, 1997.
DOI : 10.1006/jcta.1996.2711

I. M. Gelfand and M. L. Tsetlin, Finite dimensional representations of the group of unimodular matrices, Dokl. Akad. Nauk. USSR, vol.71, pp.275-290, 1981.

F. Gillet, Asymptotic behaviour of watermelons, 2003.

N. R. Goodman, Statistical Analysis Based on a Certain Multivariate Complex Gaussian Distribution (An Introduction), The Annals of Mathematical Statistics, vol.34, issue.1, pp.152-177, 1963.
DOI : 10.1214/aoms/1177704250

G. J. Heckman, Projections of orbits and asymptotic behavior of multiplicities for compact connected Lie groups, Inventiones Mathematicae, vol.6, issue.No 8, pp.333-356, 1982.
DOI : 10.1007/BF01393821

P. Heinzner, A. Huckleberry, and M. R. Zirnbauer, Symmetry Classes of Disordered Fermions, Communications in Mathematical Physics, vol.37, issue.3, pp.725-771, 2005.
DOI : 10.1007/s00220-005-1330-9

S. Helgason, Groups and Geometric Analysis, 1984.
DOI : 10.1090/surv/083

K. Johansson, Random matrices and determinantal processes, arXiv:math?ph, 5100381.

K. Johansson and E. Nordenstam, Eigenvalues of GUE Minors, Electronic Journal of Probability, vol.11, issue.0, pp.1342-1371, 2006.
DOI : 10.1214/EJP.v11-370

M. Kashiwara, On crystal bases, Representations of Groups, CMS Conference proceedings, Amer. Math. Soc, vol.16, pp.155-197, 1995.

M. Kashiwara and T. Nakashima, Crystal Graphs for Representations of the q-Analogue of Classical Lie Algebras, Journal of Algebra, vol.165, issue.2, pp.295-345, 1994.
DOI : 10.1006/jabr.1994.1114

M. Katori, H. Tanemura, T. Nagao, and N. Komatsuda, Vicious walks with a wall, noncolliding meanders, and chiral and Bogoliubov???de Gennes random matrices, Physical Review E, vol.68, issue.2, pp.21112-21113, 2003.
DOI : 10.1103/PhysRevE.68.021112

M. Katori and H. Tanemura, Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems, Journal of Mathematical Physics, vol.45, issue.8, pp.3058-3085, 2004.
DOI : 10.1063/1.1765215

M. Katori and H. Tanemura, Nonintersecting paths, noncolliding diffusion processes and representation theory, RIMS Kokyuroku, pp.1438-83, 2005.

A. A. Kirillov, Merits and demerits of the orbit method, Bulletin of the American Mathematical Society, vol.36, issue.04, pp.433-488, 1999.
DOI : 10.1090/S0273-0979-99-00849-6

A. A. Kirillov, Lectures on the orbit method, Graduate Studies in Mathematics, vol.64, 2004.
DOI : 10.1090/gsm/064

A. Klyachko, Random walks on symmetric spaces and inequalities for matrix spectra, Linear Algebra and its Applications, vol.319, issue.1-3, pp.37-59, 2000.
DOI : 10.1016/S0024-3795(00)00219-6

A. W. Knapp, Lie groups, beyond an introduction, 2002.
DOI : 10.1007/978-1-4757-2453-0

C. Krattenthaler, A. J. Guttmann, and X. G. Viennot, Vicious walkers, friendly walkers and Young tableaux: II. With a wall, Journal of Physics A: Mathematical and General, vol.33, issue.48, pp.33-48, 2000.
DOI : 10.1088/0305-4470/33/48/318

URL : http://arxiv.org/abs/cond-mat/0006367

M. L. Mehta and N. Rosenzweig, Distribution laws for the roots of a random antisymmetric hermitian matrix, Nuclear Physics A, vol.109, issue.2, pp.449-456, 1968.
DOI : 10.1016/0375-9474(68)90611-8

T. Nakashima, Crystal base and a generalization of the Littlewood-Richardson rule for the classical Lie algebras, Communications in Mathematical Physics, vol.88, issue.2, pp.215-243, 1993.
DOI : 10.1007/BF02096996

A. Okounkov and N. Reshetikhin, The birth of random matrix, Moscow Mathematical Journal, vol.6, pp.553-566, 2006.

G. Olshanski, Unitary representations of (G,K)-pairs that are connected with the infinite symmetric group S(?), Leningrad Math, J, vol.1, pp.983-1014, 1990.

G. Olshanski, Unitary representation of infinite dimensional pairs (G,K) and the formalism of R.Howe. Representation of Lie groups and related topics, Advanced Studies in Contemporary Mathematics, 1990.

G. Olshanski, The problem of harmonic analysis on the infinite-dimensional unitary group, Journal of Functional Analysis, vol.205, issue.2, pp.464-524, 2003.
DOI : 10.1016/S0022-1236(02)00022-8

G. Olshanski and A. Vershik, Ergodic unitary invariant measures on the space of infinite Hermitian matrices, Amer. Math. soc. Translations, vol.2, pp.175-137, 1996.

U. Porod, The cut-off phenomenon for random reflections, The Annals of Probability, vol.24, issue.1, pp.74-96, 1996.
DOI : 10.1214/aop/1042644708

U. Porod, The out-off phenomenon for random reflections II: Complex and quaternionic cases, Probability Theory and Related Fields, vol.217, issue.2, pp.181-209, 1996.
DOI : 10.1007/BF01247837

J. S. Rosenthal, Random Rotations: Characters and Random Walks on SO(N), The Annals of Probability, vol.22, issue.1, pp.398-423, 1994.
DOI : 10.1214/aop/1176988864

M. Roesler, Bessel convolutions on matrix cones, Compositio Mathematica, vol.143, issue.03, pp.749-779, 2007.
DOI : 10.1112/S0010437X06002594

J. J. Verbaarschot, Spectrum of the QCD Dirac operator and chiral random matrix theory, Physical Review Letters, vol.72, issue.16, pp.72-2531, 1994.
DOI : 10.1103/PhysRevLett.72.2531

D. Wang, Spiked models in Wishart Ensemble

E. P. Wigner, On the statistical distribution of the widths and spacings of nuclear resonance levels, Proc. Cambridge Philos. Soc, pp.47-790, 1951.
DOI : 10.1017/S0305004100027237

J. Wishart, THE GENERALISED PRODUCT MOMENT DISTRIBUTION IN SAMPLES FROM A NORMAL MULTIVARIATE POPULATION, Biometrika, vol.20, issue.1-2, pp.20-32, 1928.
DOI : 10.1093/biomet/20A.1-2.32

D. P. Zhelobenko, Compact Lie groups and their representations, Transl. of Math. Monographs, vol.40, 1973.