Electronic Communications in Probability

A Proof of a Non-Commutative Central Limit Theorem by the Lindeberg Method

Vladislav Kargin

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Abstract

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.

Article information

Source
Electron. Commun. Probab., Volume 12 (2007), paper no. 5, 36-50.

Dates
Accepted: 5 March 2007
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465224948

Digital Object Identifier
doi:10.1214/ECP.v12-1250

Mathematical Reviews number (MathSciNet)
MR2300213

Zentralblatt MATH identifier
1133.46037

Subjects
Primary: 46L54: Free probability and free operator algebras
Secondary: 60F05: Central limit and other weak theorems

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

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Kargin, Vladislav. A Proof of a Non-Commutative Central Limit Theorem by the Lindeberg Method. Electron. Commun. Probab. 12 (2007), paper no. 5, 36--50. doi:10.1214/ECP.v12-1250. https://projecteuclid.org/euclid.ecp/1465224948


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References

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