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arXiv · 0802.0292

An Elementary Proof of the Free-additivity of Voiculescu's Free Entropy

Don Hadwin·Weihua Li·Junhao Shen
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Abstract

D. Voiculescu [2] proved that a standard family of independent random unitary k by k matrices and a constant k by k unitary matrix is asymtotically free as k goes to infinity. This result was a key ingredient in Voiculescu's proof [3] that his free entropy is additive when the variables are free. In this paper, we give a very elementary proof of a more detailed version of this result [2].

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Don Hadwin, Weihua Li, Junhao Shen. 2008-02-03. An Elementary Proof of the Free-additivity of Voiculescu's Free Entropy. https://arxiv.org/abs/0802.0292

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