Discussions around Voiculescu's free entropies.

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2000 Mathematics Subject Classification MSC:

Abstract: In this article, we set two analoguous definitions of the free entropies chi and chi* introduced by D. Voiculescu. We discuss their relations, improving the results obtained in Large deviations upper bound..., where a bound on the microstates entropy chi was established.

keywords: Large deviations, random matrices, non-commutatitve measure, integration.