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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.

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Vladislav Kargin. 2007-03-12. A Proof of a Non-Commutative Central Limit Theorem by the Lindeberg Method. https://arxiv.org/abs/math/0703345

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