A 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.
Review:
Leonid Petrov, Random Matrices, lecture notes 2019 (pdf slides, pdf, webpage)
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
Terrence Tao, Topics in random matrix theory pdf
See also:
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 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, lecture notes (arxiv/1510.04430)
Greg W. Anderson, Alice Guionnet, Ofer Zeitouni, An Introduction to Random Matrices, Cambridge Studies in Advanced Mathematics
Random matrix theory applies to black holes in string theory:
via the SYK model:
Jordan S. Cotler, Guy Gur-Ari, Masanori Hanada, Joseph Polchinski, Phil Saad, Stephen Shenker, Douglas Stanford, Alexandre Streicher, Masaki Tezuka, Black Holes and Random Matrices, JHEP 1705:118, 2017 (arXiv:1611.04650)
Yiyang Jia, Jacobus J. M. Verbaarschot, Spectral Fluctuations in the Sachdev-Ye-Kitaev Model (arXiv:1912.11923)
via the BFSS matrix model:
via AdS/CFT for Jackiw-Teitelboim gravity:
Phil Saad, Stephen Shenker, Douglas Stanford, JT gravity as a matrix integral (arXiv:1903.11115)
Douglas Stanford, Edward Witten, JT Gravity and the Ensembles of Random Matrix Theory (arXiv:1907.03363)
Last revised on April 10, 2023 at 23:19:25. See the history of this page for a list of all contributions to it.