random matrix (Rev #5) in nLab

Random matrix is a matrix-valued random variable. Random matrix theory studies mainly the behaviour of eigenvalues and various functions of random matrices; as such it has large importance in physics.

• related entries: Calogero-Moser system, large N limit
• Madan Lal Mehta, Random matrices, 3rd ed. Pure and Applied Math. (Amsterdam) 142, Elsevier/Academic Press 2004. xviii+688 pp. MR2129906, gBooks
• wikipedia random matrix
• V. L. Girko, Theory of random determinants, Transl. from Russian (Višča Škola, Kiev 1980, MR82h:60002). Mathematics and its Applications (Soviet Series) 45, Kluwer 1990, MR1080966
• Freeman J. Dyson, Statistical theory of the energy levels of complex systems, I, J. Math. Phys. 3 1962 140–156, MR143556, doi; II, JMP 3 1962 157–165, MR143557, doi; III, JMP 3 1962 166–175, MR143558, doi; A Brownian-motion model for the eigenvalues of a random matrix, JMP 3 1962 1191–1198, MR148397, doi; Fredholm determinants and inverse scattering problems, Comm. Math. Phys. 47, 171–183 (1976) MR406201 euclid
• J J M Verbaarschot, M R Zirnbauer, Critique of the replica trick, J. Phys. A: Math. Gen. 17 (1985) 1093-1109, pdf
• Patrik L. Ferrari, Why random matrices share universal processes with interacting particle systems?, arxiv/1312.1126
• Bertrand Eynard, Taro Kimura, Sylvain Ribault, Random matrices, (lectures, 138 pages) arxiv/1510.04430
• Greg W. Anderson, Alice Guionnet, Ofer Zeitouni, An Introduction to Random Matrices, Cambridge Studies in Advanced Mathematics