Haar-Distributed Unitary Matrices
نویسنده
چکیده
We provide an elementary proof for a theorem due to Petz and Réffy which states that for a random n × n unitary matrix with distribution given by the Haar measure on the unitary group U(n), the upper left (or any other) k × k submatrix converges in distribution, after multiplying by a normalization factor √ n and as n → ∞, to a matrix of independent complex Gaussian random variables with mean 0 and variance 1. MSC(2000): 15A52; 60B10.
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