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

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

2007-12-18

arxiv.org/abs/0712.2974v1

Mathematics

Operator Algebras

14 pages

Scientific paper

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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