A new Berry-Esseen-type estimate in the free central limit theorem

Leonie Neufeld

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arXiv · 2503.23403

A new Berry-Esseen-type estimate in the free central limit theorem

Leonie Neufeld

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Abstract

Using the subordination approach, we provide a new Berry-Esseen-type estimate in the free central limit theorem in terms of the fourth Lyapunov fraction. In the special case of identical distributions, our result implies a rate of order $n^{-1/2 + \varepsilon}$ for any $\varepsilon>0$, thus almost leading to the optimal rate of order $n^{-1/2}$.

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Leonie Neufeld. 2025-03-30. A new Berry-Esseen-type estimate in the free central limit theorem. https://arxiv.org/abs/2503.23403

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