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.
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Research Article| August 11 2008
Asymptotic behavior of group integrals in the limit of infinite rank
J. Math. Phys. 19, 999–1001 (1978)
Don Weingarten; Asymptotic behavior of group integrals in the limit of infinite rank. J. Math. Phys. 1 May 1978; 19 (5): 999–1001. https://doi.org/10.1063/1.523807
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