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  • 1 Budapest University of Technology and Economics Department for Mathematical Analysis H-1521 Budapest XI. Hungary H-1521 Budapest XI. Hungary
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Let U n be an n 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.