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A Free Logarithmic Sobolev Inequality on the Circle |
Canad. Math. Bull. 49(2006), 389-406
Published:2006-09-01
Printed: Sep 2006
Printed: Sep 2006
- Fumio Hiai
- Dénes Petz
- Yoshimichi Ueda
Abstract
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 - Free probability and free operator algebras 60E15 - Inequalities; stochastic orderings 94A17 - Measures of information, entropy |