Brownian-motion ensembles: correlation functions of determinantal processes

Abstract

We calculate the n-point correlation function for a large class of Brownian-motion ensembles of random matrix theory. The corresponding Fokker–Planck equation describes a determinantal process in the theory of matrix-valued stochastic differential equations and can be mapped onto a Schödinger equation of non-interacting electrons in one dimension. The correlation functions are obtained explicitly via a suitable generalization of the method of biorthogonal functions.