A proof of a non-commutative central limit theorem by the Lindeberg method

被引：0

作者：

Kargin, Vladislav ^{[1
]}

机构：

[1] Courant Inst Math Sci, Forest Hills, NY 11375 USA

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2007年 / 12卷

关键词：

central limit theorem; Lindeberg method; free probability; free convolution; free independence;

D O I：

暂无

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：

A Central Limit Theorem for non-commutative random variables is proved using the Lindeberg method. The theorem is a generalization of the Central Limit Theorem for free random variables proved by Voiculescu. The Central Limit Theorem in this paper relies on an assumption which is weaker than freeness.

引用

页码：44 / 58

页数：15

共 50 条

[41] Limit algebras of differential forms in non-commutative geometry
Bhatt, S. J.
Inoue, A.
[J]. PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2008, 118 (03): : 425 - 441
[42] An analogue of Peetre's theorem in non-commutative topology
Schweizer, J
[J]. QUARTERLY JOURNAL OF MATHEMATICS, 2001, 52 : 499 - 506
[43] An extension of a non-commutative Choquet-Deny theorem
Willis, GA
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 128 (01) : 111 - 118
[44] EASY THEOREM IN NON-COMMUTATIVE STATISTICAL-MECHANICS
LUBKIN, E
[J]. BULLETIN OF THE AMERICAN PHYSICAL SOCIETY, 1976, 21 (01): : 115 - 115
[45] PCT theorem in field theory on non-commutative space
Mahajan, N
[J]. PHYSICS LETTERS B, 2003, 569 (1-2) : 85 - 89
[46] LIMIT THEOREMS FOR NON-COMMUTATIVE OPERATIONS .1.
BELLMAN, R
[J]. DUKE MATHEMATICAL JOURNAL, 1954, 21 (03) : 491 - 500
[47] Limit algebras of differential forms in non-commutative geometry
S. J. Bhatt
A. Inoue
[J]. Proceedings Mathematical Sciences, 2008, 118 : 425 - 441
[48] Non-commutative automorphisms of bounded non-commutative domains
McCarthy, John E.
Timoney, Richard M.
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2016, 146 (05) : 1037 - 1045
[49] Dependent Lindeberg central limit theorem for the fidis of empirical processes of cluster functionals
Gomez, Jose G.
[J]. STATISTICS, 2018, 52 (05) : 955 - 979
[50] A NON-ELEMENTARY PROOF BY DIFFERENTIAL EQUATION FOR THE CENTRAL LIMIT THEOREM
Korkmaz, Adil
Onemli, Muharrem Burak
[J]. PAKISTAN JOURNAL OF STATISTICS, 2013, 29 (03): : 307 - 313

← 1 2 3 4 5 →