Integration over matrix spaces with unique invariant measures
Mathematical Physics
2015-06-26 v1 math.MP
Chaotic Dynamics
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.
Keywords
Cite
@article{arxiv.math-ph/0203042,
title = {Integration over matrix spaces with unique invariant measures},
author = {T. Prosen and T. H. Seligman and H. A. Weidenmueller},
journal= {arXiv preprint arXiv:math-ph/0203042},
year = {2015}
}
Comments
12 pages in revtex, no figures