Berry-Esseen for Free Random Variables

Details Berry-Esseen for Free Random Variables Berry-Esseen for Free Random Variables

2006-10-02

arxiv.org/abs/math/0610072v3

Journal of Theoretical Probability, 2007, 20, 381-395

Mathematics

Probability

15 pages, accepted to the Journal of Theoretical Probability, minor typos are corrected in versions 2 and 3

Scientific paper

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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