Don Hadwin, Weihua Li, Junhao Shen
Published 2008-02-03Version 1
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].
Concavification of free entropy
Inequality for Voiculescu's free entropy in terms of Brown measure
An Elementary Proof of the Inequality $χ\leq χ^*$ for Conditional Free Entropy
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