Electronic Communications in Probability

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

Vladislav Kargin

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

central limit theorem Lindeberg method free probability free convolution free independence

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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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