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Berry–Esseen for Free Random Variables

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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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Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, 109-20 71st Road, Apt. 4A, New York, NY, 11375, USA

    Vladislav Kargin

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  1. Vladislav Kargin
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Correspondence to Vladislav Kargin.

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V. Kargin is grateful to Diana Bloom for her help with editing this paper.

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Kargin, V. Berry–Esseen for Free Random Variables. J Theor Probab 20, 381–395 (2007). https://doi.org/10.1007/s10959-007-0097-7

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  • DOI: https://doi.org/10.1007/s10959-007-0097-7

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