GENERAL MOMENTS OF MATRIX ELEMENTS FROM CIRCULAR ORTHOGONAL ENSEMBLES
SHO MATSUMOTO · Random Matrices Theory and Application · 2012
The aim of this paper is to present a systematic method for computing moments of matrix elements taken from circular orthogonal ensembles (COE). The formula is given as a sum of Weingarten functions for orthogonal groups but the technique for its proof involves Weingarten calculus for unitary groups. As an application, explicit expressions for the moments of a single matrix element of a COE matrix are given.