Matrices aléatoires : généralités

  • The Oxford Handbook of Random Matrix Theory, Edited by G. Akemann, J. Baik, P. Di Francesco, Oxford University Press, 2011.
  • An Introduction to Random Matrices, G. Anderson, A. Guionnet, O. Zeitouni, Cambridge University Press, 2009. here.
  • Spectral analysis of large dimensional random matrices, Z.D. Bai, J.W. Silverstein Second Edition, Springer, New York, 2009.
  • Topics in Random Matrix Theory, T. Tao, Graduate Studies in Mathematics, AMS, 2012.
  • Eigenvalue Distribution of Large Random Matrices, L. Pastur, M. Shcherbina, Mathematical Surveys and Monographs, AMS, 2011.
  • Notes on random matrices, C. Bordenave. here.
  • Around the circular law, C. Bordenave, D. Chafaï, here.
  • Several applications of the moment method in random matrix theory, S. Sodin, Proc. International Congress of Mathematicians 2014. here.
  • Lecture Notes on Random Matrices, V. Kargin, E. Yudovina, here.

Matrices aléatoires : aspect systèmes intégrables

  • Random Matrices, M.L. Mehta. Second Edition, Academic Press, Boston, 1991.
  • Log-gases and random matrices, P. J. Forrester, Princeton University Press, Princeton, NJ, 2010.
  • Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, P. Deift, Courant Lecture Notes, AMS, 2000.
  • Random Matrix Theory: Invariant Ensembles and Universality, P. Deift, D. Gioev, Courant Lecture Notes, AMS, 2009.
  • A Survey on the Eigenvalues Local Behavior of Large Complex Correlated Wishart Matrices, W. Hachem, A. Hardy, J. Najim, ESAIM: Proceedings and Surveys, 2015. here.
  • The Surprising Mathematics of Longest Increasing Subsequences, D. Romik, Cambridge University press, 2015. here.
  • Combinatorics and Random Matrix Theory, J. Baik, P. Deift, T. Suidan, Graduate Studies in Mathematics, AMS, 2016.
  • Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem, D. Aldous, P. Diaconis, Bull. Amer. Math. Soc. (N.S.) 36 (1999), no. 4, 413–432.
  • Lectures on integrable probability, A. Borodin, V. Gorin. here.
  • Random matrices and determinant processes, K. Johansson, Mathematical statistical physics, 1–55, Elsevier B. V., Amsterdam, 2006. here.
  • Kardar-Parisi-Zhang universality, I. Corwin, Notices Amer. Math. Soc. 63 (2016), no. 3, 230–239. here.
  • Random matrices, B. Valko (with Valko-Virag's approach to beta-ensembles). here.

Matrices aléatoires : liens avec les probabilités libres

  • Free probability for probabilists, P. Biane, MSRI Publications, 1998. here.
  • Lectures on the combinatorics of free probability, A. Nica, R. Speicher. Cambridge University Press, Cambridge, 2006.
  • The Semicircle Law, Free Random Variables and Entropy, F. Hiai, D. Petz, Mathematical Surveys and Monographs, 2000.
  • Free random variables, D. Voiculescu, K. Dykema, A. Nica, CRM Monograghs Series No.1, Amer. Math. Soc., Providence, RI, 1992.
  • Large Random Matrices: Lectures on Macroscopic Asymptotics, A. Guionnet, École d'Été de Probabilités de Saint-Flour XXXVI – 2006.
  • Free probability and random matrices, R. Speicher, Proc. International Congress of Mathematicians 2014. here.
  • Free probability and random matrices, J. A. Mingo and R. Speicher, ongoing project. here
  • Three lectures on free probability, J. Novak, M. LaCroix. here.
  • Lecture Notes on Free Probability, V. Kargin, here.
  • What is Free Probability?, R. Speicher, here.

Matrices aléatoires : lois locales

  • Universality for random matrices and log-gases, L. Erdös, 2012. here.
  • Universality of local spectral statistics of random matrices, L. Erdös, H.-T. Yau, Bull. Amer. Math. Soc. 49(3), 377-414. here.
  • Dynamical approach to random matrix theory, L. Erdös, H.-T. Yau (ongoing project). here.
  • Lectures on the local semicircle law for Wigner matrices, F. Benaych-Georges, A. Knowles. To appear in SMF volume Panoramas et Synthèses (2017). here.

Graphes aléatoires

  • Random graphs, B. Bollobas, Cambridge University Press, 2009.
  • Spectral Graph Theory, F. Chung, CBMS Regional Conference Series in Mathematics, 1997.
  • Spectral measures of random graphs, C. Bordenave. To appear in SMF volume Panoramas et Synthèses (2017). here.

Matrices aléatoires et physique mathématique

  • Alice and Bob meet Banach (The Interface of Asymptotic Geometric Analysis and Quantum Information Theory), G. Auburn, S. Szarek (ongoing project). here.
  • Two-dimensional Markovian holonomy fields, T. Lévy, 2008. here.

Matrices aléatoires : applications aux télécommunications

  • Random Matrix Theory and Wireless Communications, A. Tulino, S. Verdu, 2004.
  • Random Matrix Methods for Wireless Communications, R. Couillet, M. Debbah, Cambridge University Press, 2011.

Matrices aléatoires : applications aux statistiques

  • Four lectures on probabilistic methods for data science, R. Vershynin. 2016 PCMI Summer School, AMS. here
  • Textbook in high dimensional probability with applications in data science, ongoing project, R. Vershynin. here
  • Introduction to the non-asymptotic analysis of random matrices, R. Vershynin, Compressed sensing, 210–268, Cambridge University Press, 2012. here
  • Interactions between compressed sensing, random matrices, and high dimensional geometry, D. Chafaï, O. Guédon, G. Lécué, A. Pajor. Panoramas et Synthèses 37, SMF, 2012. here.
  • An Introduction to Matrix Concentration Inequalities, J. A. Tropp. Found. Trends Mach. Learning, Vol. 8, num. 1-2, pp. 1-230, May 2015. here.
  • High Dimensional Statistics, P. Rigollet, here.
  • Ten lectures and forty-two open problems in the mathematics of data science, A. Bandeira here.
  • A Mathematical Introduction to Compressive Sensing, S. Foucart, H. Rauhut, Birkäuser, 2013.
  • Introduction to High-Dimensional Statistics, C. Giraud, CRC Press, 2014.
  • High Dimensional Statistical Inference and Random Matrices, I. M. Johnstone, Proc. International Congress of Mathematicians 2006, 307-333. here.

Outils de la concentration et du transport appliqués aux matrices aléatoires

  • Random matrices: high dimensional phenomena, G. Blower, London Mathematical Society, 2009.
  • The Concentration of Measure Phenomenon, M. Ledoux, AMS, 2005.
  • Concentration Inequalities: A Nonasymptotic Theory of Independence, S. Boucheron, G. Lugosi, P. Massart, Oxford Univ. Press, 2013.
  • A transportation approach to universality in random matrix theory, A. Figalli, Boll. Unione Mat. Ital., 10 (2017), no. 1, 55-74. here.
  • mega/gdr/bib.txt
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