Discussions around Voiculescu's free entropies |
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| Authors: | Thierry Cabanal-Duvillard Alice Guionnet |
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| Affiliation: | a UFR Math.Info., Université René Descartes, 45 rue des St Pères, Paris 5, Cedex 06 75270, France
b UMPA, Ecole Normale Supérieure de Lyon, 46 allée d'Italie, Lyon 69007, France |
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| Abstract: | In this article, we set two analogous definitions of the free entropies χ and χ∗ introduced by Voiculescu (Invent. Math. 118 (1994) 411; 132 (1998) 189). We discuss their relations, improving the preceding results obtained in Cabanal-Duvillard and Guionnet (Ann. Probab. (2001), to appear), where a bound on the microstates entropy χ was established. |
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| Keywords: | 60F10 15A52 46L50 |
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