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 - Bertrand Eynard, Taro Kimura, Sylvain Ribault,
*Random matrices*, (lectures, 138 pages) arxiv/1510.04430

Revised on April 13, 2016 15:08:32
by Zoran Škoda
(161.53.28.4)