General moments of matrix elements from circular orthogonal ensembles
Sho Matsumoto
TL;DR
This paper develops a systematic method to compute moments of matrix elements from circular orthogonal ensembles using Weingarten calculus, providing explicit formulas and advancing understanding of COE matrix statistics.
Contribution
It introduces a novel approach combining Weingarten calculus for orthogonal and unitary groups to compute moments in COE matrices.
Findings
Explicit formulas for moments of COE matrix elements
Method unifies orthogonal and unitary Weingarten calculus
Provides tools for statistical analysis of COE matrices
Abstract
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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