Free entropy

被引：73
作者：
Voiculescu, D [1 ]
机构：
[1] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA
来源：
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2002年 / 34卷
基金：
美国国家科学基金会;
关键词：
D O I：
10.1112/S0024609301008992
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Free entropy is the analogue of entropy in free probability theory. The paper is a survey of free entropy, its applications to von Neumann algebras and its connections to random matrix theory, as well as a discussion of open problems and of a basic variational problem, connected to random multimatrix models.
引用
收藏
页码：257 / 278
页数：22
相关论文
共 56 条
[1]  
[Anonymous], 1969, ALGEBRES OPERATEURS
[2]  
[Anonymous], 1997, FIELDS I COMMUN
[3]   ENTROPY AND THE CENTRAL-LIMIT-THEOREM [J].
BARRON, AR .
ANNALS OF PROBABILITY, 1986, 14 (01) :336-342
[4]  
BenArous G, 1997, PROBAB THEORY REL, V108, P517
[5]  
Biane P, 2001, GEOM FUNCT ANAL, V11, P1125
[6]   Free diffusions, free entropy and free Fisher information [J].
Biane, P ;
Speicher, R .
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2001, 37 (05) :581-606
[7]  
Biane P., 1997, Free Probability Theory, V12, P1
[8]   ENTROPY PRODUCTION BY BLOCK VARIABLE SUMMATION AND CENTRAL LIMIT-THEOREMS [J].
CARLEN, EA ;
SOFFER, A .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1991, 140 (02) :339-371
[9]   SUPERADDITIVITY OF FISHER INFORMATION AND LOGARITHMIC SOBOLEV INEQUALITIES [J].
CARLEN, EA .
JOURNAL OF FUNCTIONAL ANALYSIS, 1991, 101 (01) :194-211
[10]  
Cover T. M., 2005, ELEM INF THEORY, DOI 10.1002/047174882X
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