ENSEMBLES OF HERMITIAN RANDOM MATRICES ASSOCIATED TO SYMMETRIC SPACES

Classical physics-inspired random matrix theory had its focus on ensembles of hermitian, real symmetric, or real quaternionic matrices, which may be viewed as probability measures on the tangent spaces to the classical symmetric spaces of class A, AI or AII. Condensed matter physics provides some motivation to extend this theory to the full list of classical symmetric spaces. This contribution discusses the basic strategies to randomize matrices in this broader setting, and reviews our results in Refs. 1 (joint work with Katrin Hofmann-Credner) and 2 (joint work with Peter Eichelsbacher) on the empirical eigenvalue measure for matrix size tending to infinity.