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On asymptotics of large Haar distributed unitary matrices

Denes Petz·Julia Reffy
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Abstract

Let $U_n$ be an $n \times n$ Haar unitary matrix. In this paper, the asymptotic normality and independence of $\Tr U_n, \Tr U_n^2, ..., \Tr U_n^k$ are shown by using elementary methods. More generally, it is shown that the renormalized truncated Haar unitaries converge to a Gaussian random matrix in distribution.

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Denes Petz, Julia Reffy. 2003-10-21. On asymptotics of large Haar distributed unitary matrices. https://arxiv.org/abs/math/0310338

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