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arXiv · 0705.3146

Elementary Proof for Asymptotics of Large Haar-Distributed Unitary Matrices

Christian Mastrodonato·Roderich Tumulka
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Abstract

We provide an elementary proof for a theorem due to Petz and Réffy which states that for a random $n\times n$ unitary matrix with distribution given by the Haar measure on the unitary group U(n), the upper left (or any other) $k\times k$ submatrix converges in distribution, after multiplying by a normalization factor $\sqrt{n}$ and as $n\to\infty$, to a matrix of independent complex Gaussian random variables with mean 0 and variance 1.

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Christian Mastrodonato, Roderich Tumulka. 2007-10-03. Elementary Proof for Asymptotics of Large Haar-Distributed Unitary Matrices. https://doi.org/10.1007/s11005-007-0194-7

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