A log-Sobolev type inequality for free entropy of two projections

被引：9

作者：

Hiai, Fumio ^{[1
]}

Ueda, Yoshimichi ^{[2
]}

机构：

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

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

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2009年 / 45卷 / 01期

基金：

日本学术振兴会;

关键词：

Logarithmic Sobolev inequality; Free entropy; Mutual free Fisher information; FREE PROBABILITY-THEORY; FISHER INFORMATION MEASURE; ANALOGS;

D O I：

10.1214/08-AIHP164

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove a kind of logarithmic Sobolev inequality claiming that the mutual free Fisher information dominates the microstate free entropy adapted to projections in the case of two projections.

引用

页码：239 / 249

页数：11

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