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arXiv · 1202.2740

Operator-valued and multivariate free Berry-Esseen theorems

Tobias Mai·Roland Speicher
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Abstract

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. Since we have to deal with in general non-self-adjoint operators, we introduce the notion of matrix-valued resolvent sets and study the behavior of Cauchy transforms on them.

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Tobias Mai, Roland Speicher. 2012-02-13. Operator-valued and multivariate free Berry-Esseen theorems. https://arxiv.org/abs/1202.2740

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