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On the rate of convergence and Berry-Esseen type theorems for a multivariate free central limit theorem

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arxiv 0712.2974 v1 pith:2DIV5OMC submitted 2007-12-18 math.OA

Roland Speicher This is my paper · ORCID
classification math.OA
keywords theoremcentralfreelimitoperator-valuedcauchyconvergencemultivariate
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We address the question of a Berry Esseen type theorem for the speed of convergence in a multivariate free central limit theorem. For this, we estimate the difference between the operator-valued Cauchy transforms of the normalized partial sums in an operator-valued free central limit theorem and the Cauchy transform of the limiting operator-valued semicircular element.

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  1. Rates of convergence in the Free Multiplicative Central Limit Theorem

    math.OA 2025-05 conditional novelty 8.0 of 10

    First quantitative convergence rates for the free multiplicative CLT in Wasserstein and Kolmogorov distances.

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