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#### Integration over matrix spaces with unique invariant measures

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##### Citation

Prosen, T., Seligman, T. H., & Weidenmüller, H. A. (2002). Integration over matrix
spaces with unique invariant measures.* Journal of Mathematical Physics,* *43*(10),
5135-5144.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0011-828F-1

##### Abstract

We present a method to calculate integrals over monomials of matrix elements with invariant measures in terms of Wick contractions. The method gives exact results for monomials of low order. For higher-order monomials, it leads to an error of order 1/N-alpha, where N is the dimension of the matrix and where alpha is independent of the degree of the monomial. We give a lower bound on the integer alpha and show how alpha can be increased systematically. The method is particularly suited for symbolic computer calculation. Explicit results are given for O(N), U(N), and for the circular orthogonal ensemble. (C) 2002 American Institute of Physics.