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The analogues of entropy and of Fisher's information measure in free probability theory, I

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Abstract

Analogues of the entropy and Fisher information measure for random variables in the context of free probability theory are introduced. Monotonicity properties and an analogue of the Cramer-Rao inequality are proved.

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Author notes

  1. Dan Voiculescu

    Present address: Department of Mathematics, University of California, 94720, Berkeley, CA, USA

Authors and Affiliations

  1. I.H.E.S., F-91440, Bures-sur-Yvette, France

    Dan Voiculescu

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  1. Dan Voiculescu
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Additional information

Communicated by A. Jaffe

Dedicated to Huzuhiro Araki

Work supported in part by a Grant from the National Science Foundation

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Voiculescu, D. The analogues of entropy and of Fisher's information measure in free probability theory, I. Commun.Math. Phys. 155, 71–92 (1993). https://doi.org/10.1007/BF02100050

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  • DOI: https://doi.org/10.1007/BF02100050

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