Lectures on random matrix theory and symmetric spaces

Abstract

In these lectures we discuss some elementary concepts in connection with the theory of symmetric spaces applied to ensembles of random matrices. We review how the relationship between random matrix theory and symmetric spaces can be used in some physical contexts.

Invited lectures presented at the UK-Japan Winter School "Geometric, Spectral, and Stochastic Analysis", Evesham, UK, January 2005; 72 pages, 8 figures