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Berry-Esseen for Free Random Variables

Vladislav Kargin
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Abstract

An analogue of the Berry-Esseen inequality is proved for the speed of convergence of free additive convolutions of bounded probability measures. The obtained rate of convergence is of the order n^{-1/2}, the same as in the classical case. An example with binomial measures shows that this estimate cannot be improved without imposing further restrictions on convolved measures.

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Vladislav Kargin. 2006-10-09. Berry-Esseen for Free Random Variables. https://arxiv.org/abs/math/0610072

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