Asymptotic behavior of group integrals in the limit of infinite rank

Abstract

We show that in the limit N→∞ integrals with respect to Haar measure of products of the elements of a matrix in SO(N) approach corresponding moments of a set of independent Gaussian random variables. Similar asymptotic forms are obtained for SU(N) and Sp(N). An application of these results to Wilson’s formulation of lattice gauge theory is briefly considered.