Riemannian symmetric superspaces and their origin in random-matrix theory

Gaussian random matrix ensembles defined over the tangent spaces of the largefamilies of Cartan's symmetric spaces are considered. Such ensembles play acentral role in mesoscopic physics since they describe the universal ergodiclimit of disordered and chaotic single particle systems. The generatingfunction for the spectral correlations of each ensemble is reduced to anintegral over a Riemannian symmetric superspace in the limit of large matrixdimension. Such a space is defined as a pair (G/H,M_r) where G/H is acomplex-analytic graded manifold homogeneous with respect to the action of acomplex Lie supergroup G, and M_r is a maximal Riemannian submanifold of thesupport of G/H.Comment: 27 pages, LaTe