Communications in Mathematical Physics

, Volume 155, Issue 1, pp 71–92 | Cite as

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

  • Dan Voiculescu


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.


Entropy Neural Network Statistical Physic Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Dan Voiculescu
    • 1
  1. 1.I.H.E.S.Bures-sur-YvetteFrance

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