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.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 May 1978
 DOI:
 10.1063/1.523807
 Bibcode:
 1978JMP....19..999W
 Keywords:

 02.30.Sa;
 02.20.Qs;
 Functional analysis;
 General properties structure and representation of Lie groups