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A Free Logarithmic Sobolev Inequality on the Circle

Open Access article
 Printed: Sep 2006
  • Fumio Hiai
  • Dénes Petz
  • Yoshimichi Ueda
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Free analogues of the logarithmic Sobolev inequality compare the relative free Fisher information with the relative free entropy. In the present paper such an inequality is obtained for measures on the circle. The method is based on a random matrix approximation procedure, and a large deviation result concerning the eigenvalue distribution of special unitary matrices is applied and discussed.
MSC Classifications: 46L54, 60E15, 94A17 show english descriptions Free probability and free operator algebras
Inequalities; stochastic orderings
Measures of information, entropy
46L54 - Free probability and free operator algebras
60E15 - Inequalities; stochastic orderings
94A17 - Measures of information, entropy

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