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 Terence Tao, Topics in random matrix...