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random matrix

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

Revised on December 5, 2013 08:31:13 by Zoran Škoda (161.53.130.104)