General moments of matrix elements from circular orthogonal ensembles

Details General moments of matrix elements from circular orthogonal ensembles General moments of matrix elements from circular orthogonal ensembles

2011-09-12

arxiv.org/abs/1109.2409v1

Mathematics

Probability

19 pages

Scientific paper

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.

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