A free logarithmic Sobolev inequality on the circle

被引：3

作者：

Hiai, Fumio ^{[1
]}

Petz, Denes

Ueda, Yoshimichi

机构：

[1] Tohoku Univ, Grad Sch Informat Sci, Aoba Ku, Sendai, Miyagi 9808579, Japan

[2] Hungarian Acad Sci, Alfred Renyi Inst Math, H-1053 Budapest, Hungary

[3] Kyushu Univ, Grad Sch Math, Fukuoka 8108560, Japan

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2006年 / 49卷 / 03期

关键词：

D O I：

10.4153/CMB-2006-039-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：389 / 406

页数：18

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