Abstract
Let U n be an n × n Haar unitary matrix. In this paper, the asymptotic normality and independence of Tr U n , Tr U 2 n ,..., Tr U k n 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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Petz, D., Réffy, J. On asymptotics of large Haar distributed unitary matrices. Periodica Mathematica Hungarica 49, 103–117 (2004). https://doi.org/10.1023/B:MAHU.0000040542.56072.ab
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DOI: https://doi.org/10.1023/B:MAHU.0000040542.56072.ab