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arXiv · 1104.3614

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

Sho Matsumoto
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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.

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Sho Matsumoto. 2012-09-24. Moments of a single entry of circular orthogonal ensembles and Weingarten calculus. https://doi.org/10.1007/s11005-012-0587-0

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