Geodesic
A Free Logarithmic Sobolev Inequality on the Circle
Canadian mathematical bulletin, Tome 49 (2006) no. 3, pp. 389-406

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DOI

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.
DOI : 10.4153/CMB-2006-039-7
Mots-clés : 46L54, 60E15, 94A17 
Hiai, Fumio; Petz, Dénes; Ueda, Yoshimichi. A Free Logarithmic Sobolev Inequality on the Circle. Canadian mathematical bulletin, Tome 49 (2006) no. 3, pp. 389-406. doi: 10.4153/CMB-2006-039-7
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     author = {Hiai, Fumio and Petz, D\'enes and Ueda, Yoshimichi},
     title = {A {Free} {Logarithmic} {Sobolev} {Inequality} on the {Circle}},
     journal = {Canadian mathematical bulletin},
     pages = {389--406},
     year = {2006},
     volume = {49},
     number = {3},
     doi = {10.4153/CMB-2006-039-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-039-7/}
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