ORBITAL APPROACH TO MICROSTATE FREE ENTROPY

被引：14

作者：

Hiai, Fumio ^{[1
]}

Miyamoto, Takuho ^{[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：

INTERNATIONAL JOURNAL OF MATHEMATICS | 2009年 / 20卷 / 02期

关键词：

Free probability; free entropy; free entropy dimension; mutual free information; non-commutative random variable; free unitary Brownian motion; FREE PROBABILITY-THEORY; VON-NEUMANN-ALGEBRAS; FISHERS INFORMATION; RANDOM MATRICES; FREE-PRODUCTS; DIMENSION; ANALOGS; INEQUALITY; COST;

D O I：

10.1142/S0129167X09005261

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Motivated by Voiculescu's liberation theory, we introduce the orbital free entropy chi(orb) for non-commutative self-adjoint random variables (also for "hyperfinite random multivariables"). Besides its basic properties, the relation of chi(orb) with the usual free entropy. is shown. Moreover, the dimension counterpart delta(0,orb) of chi(orb) is discussed, and we obtain the relation between delta(0,orb) and the original free entropy dimension delta(0) together with applications to delta(0) itself.

引用

页码：227 / 273

页数：47

共 24 条

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