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A new Berry-Esseen-type estimate in the free central limit theorem
Leonie Neufeld · 2025-03-30 · via math.PR updates on arXiv.org

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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