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.

K. G.
Phys. Rev. D
K. G. Wilson, in Gauge Theories and Modern Field Theory, edited by R. Arnowitt and P. Nath (M.I.T. Press, Cambridge, Mass., 1975).
I am grateful to A. Lenard for calling my attention to this result.
A proof for the ease of a single random variable is given by M. Loève, Probability Theory (Van Nostrand, New York, 1955), p. 185.
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