Moments of a single entry of circular orthogonal ensembles and Weingarten calculus

Abstract

Consider a symmetric unitary random matrix $V=(v_{ij}{)}_{1\le i,j\le N}$ from a circular orthogonal ensemble. In this paper, we study moments of a single entry $v_{ij}$. For a diagonal entry $v_{ii}$ we give the explicit values of the moments, and for an off-diagonal entry $v_{ij}$ we give leading and subleading terms in the asymptotic expansion with respect to a large matrix size $N$. Our technique is to apply the Weingarten calculus for a Haar-distributed unitary matrix.

17 pages

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Cited by in corpus (3)

• Weingarten calculus for matrix ensembles associated with compact symmetric spaces
• Approximate orthogonality of permutation operators, with application to quantum information
• Matrix Units in the Symmetric Group Algebra, and Unitary Integration