Berry-Esseen for Free Random Variables
arXiv:math/0610072
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.
15 pages, accepted to the Journal of Theoretical Probability, minor typos are corrected in versions 2 and 3