Grandes matrices aléatoires et théorèmes d'universalité [d'après Erdos, Schlein, Tao, Vu et Yau]
Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026, Astérisque, no. 339 (2011), Exposé no. 1019, 35 p.
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Guionnet, Alice. Grandes matrices aléatoires et théorèmes d'universalité [d'après Erdos, Schlein, Tao, Vu et Yau], dans Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026, Astérisque, no. 339 (2011), Exposé no. 1019, 35 p. http://www.numdam.org/item/AST_2011__339__203_0/

[1] G. Anderson, A. Guionnet & O. Zeitouni - An introduction to random matrices, Studies adv. math., vol. 118, Cambridge Univ. Press, 2009. | MR | Zbl

[2] A. Auffinger, G. Ben Arous & S. Péché - Poisson convergence for the largest eigenvalues of heavy tailed random matrices, Ann. Inst. Henri Poincaré Probab. Stat. 45 (2009), p. 589-610. | DOI | EuDML | Numdam | MR | Zbl

[3] D. Bakry & M. Émery - Diffusions hypercontractives, in Séminaire de probabilités, XIX, 1983/84, Lecture Notes in Math., vol. 1123, Springer, 1985, p. 177-206. | DOI | EuDML | Numdam | MR | Zbl

[4] E. Brézin & S. Hikami - Correlations of nearby levels induced by a random potential, Nuclear Phys. B 479 (1996), p. 697-706. | DOI | MR | Zbl

[5] E. Brézin & S. Hikami, Spectral form factor in a random matrix theory, Phys. Rev. E 55 (1997), p. 4067-4083. | MR

[6] P. Deift & D. Gioev - Random matrix theory : invariant ensembles and universality, Courant Lecture Notes in Math., vol. 18, Courant Institute of Mathematical Sciences, New York, 2009. | MR | Zbl

[7] P. Deift, T. Kriecherbauer, K. T.-R. Mclaughlin, S. Venakides & X. Zhou - Strong asymptotics of orthogonal polynomials with respect to exponential weights, Comm. Pure Appl. Math. 52 (1999), p. 1491-1552. | DOI | MR | Zbl

[8] F. J. Dyson - A Brownian-motion model for the eigenvalues of a random matrix, J. Mathematical Phys. 3 (1962), p. 1191-1198. | DOI | MR | Zbl

[9] L. Erdős, S. Péché, J. A. Ramírez, B. Schlein & H.-T. Yau - Bulk Universality for Wigner Matrices, Comm. Pure Appl. Math. 63 (2010), p. 895-925. | MR | Zbl

[10] L. Erdős, J. A. Ramírez, B. Schlein & T. Tao, V. Vu & V. Vu, H.-T. Yau - Bulk universality for Wigner Hermitian matrices with subexponential decay, Math. Res. Lett. 17 (2010), p. 667-674. | DOI | MR | Zbl

[11] L. Erdős, , J. A. Ramírez, B. Schlein & H.-T. Yau - Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation, Electron. J. Probab. 15 (2010), p. 526-603. | DOI | MR | Zbl

[12] L. Erdős, B. Schlein & H.-T. Yau - Local Semicircle law and complete delocalization for Wigner random matrices, Comm. Math. Phys. 287 (2009), p. 641-655. | DOI | MR | Zbl

[13] L. Erdős, B. Schlein & H.-T. Yau, Wegner estimate and level repulsion for Wigner random matrices, Int. Math. Res. Not. 2010 (2010), p. 436-479. | DOI | MR | Zbl

[14] L. Erdős, B. Schlein & H.-T. Yau, Universality of random matrices and local relaxation flow, prépublication arXiv :0907.5605. | DOI | MR | Zbl

[15] L. Erdős, B. Schlein, H.-T. Yau & J. Yin - The local relaxation flow approach to universality of the local statistics for random matrices, prépublication arXiv :0911.3687. | DOI | Numdam | MR | Zbl

[16] L. Erdős, H.-T. Yau & J. Yin - Bulk universality for generalized Wigner matrices, prépublication arXiv : 1001.3453. | DOI | MR | Zbl

[17] P. J. Forrester - The spectrum edge of random matrix ensembles, Nuclear Phys. B 402 (1993), p. 709-728. | DOI | MR | Zbl

[18] D. L. Hanson & F. T. Wright - A bound on tail probabilities for quadratic forms in independent random variables, Ann. Math. Statist. 42 (1971), p. 1079-1083. | DOI | MR | Zbl

[19] Harish-Chandra - Fourier transforms on a semisimple Lie algebra. I, Amer. J. Math. 79 (1957), p. 193-257. | DOI | MR | Zbl

[20] C. Itzykson & J. B. Zuber - The planar approximation. II, J. Math. Phys. 21 (1980), p. 411-421. | DOI | MR | Zbl

[21] K. Johansson - Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices, Comm. Math. Phys. 215 (2001), p. 683-705. | DOI | MR | Zbl

[22] K. Johansson, Universality for certain Hermitian Wigner matrices under weak moment conditions, prépublication arXiv :0910.4467. | DOI | Numdam | MR | Zbl

[23] O. Khorunzhiy - High moments of large Wigner random matrices and asymptotic properties of the spectral norm, prépublication arXiv :0907.3743. | DOI | MR | Zbl

[24] M. L. Mehta - Random matrices, Pure and Applied Math., vol. 142, Elsevier/Academic Press, 2004. | MR | Zbl

[25] S. Péché - Universality in the bulk of the spectrum for complex sample covariance matrices, prépublication arXiv : 0912.2493. | DOI | Numdam | MR | Zbl

[26] S. Péché & A. Soshnikov - Wigner random matrices with non-symmetrically distributed entries, J. Stat. Phys. 129 (2007), p. 857-884. | DOI | MR | Zbl

[27] A. Ruzmaikina - Universality of the edge distribution of eigenvalues of Wigner random matrices with polynomially decaying distributions of entries, Comm. Math. Phys. 261 (2006), p. 277-296. | DOI | MR | Zbl

[28] Y. Sinai & A. Soshnikov - Central limit theorem for traces of large random symmetric matrices with independent matrix elements, Bol. Soc. Brasil. Mat. (N.S.) 29 (1998), p. 1-24. | DOI | MR | Zbl

[29] A. Soshnikov - Universality at the edge of the spectrum in Wigner random matrices, Comm. Math. Phys. 207 (1999), p. 697-733. | DOI | MR | Zbl

[30] T. Tao & V. Vu - Random matrices : universality of local eigenvalue statistics up to the edge, Comm. Math. Phys. 298 (2010), p. 549-572. | DOI | MR | Zbl

[31] T. Tao & V. Vu, Random covariance matrices : universality of local statistics of eigenvalues, prepublication arXiv :0912.0966. | DOI | MR | Zbl

[32] T. Tao & V. Vu, Random matrices : universality of local eigenvalue statistics, prepublication arXiv : 0906.0510. | DOI | MR | Zbl

[33] C. A. Tracy & H. Widom - Level-spacing distributions and the Airy kernel, Comm. Math. Phys. 159 (1994), p. 151-174. | DOI | MR | Zbl

[34] C. A. Tracy & H. Widom, The distribution of the largest eigenvalue in the Gaussian ensembles : β=1,2,4, in Calogero-Moser-Sutherland models (Montreal, QC, 1997), CRM Ser. Math. Phys., Springer, 2000, p. 461-472. | DOI | MR

[35] C. Villani - Topics in optimal transportation, Graduate Studies in Math., vol. 58, Amer. Math. Soc., 2003. | MR | Zbl

[36] E. P. Wigner - Characteristic vectors of bordered matrices with infinite dimensions, Ann. of Math. 62 (1955), p. 548-564. | DOI | MR | Zbl

[37] J. Wishart - The Generalized product moment distribution in samples from a normal multivariate population, Biometrika 20A (1928), p. 32-52. | DOI | JFM