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A new Berry-Esseen-type estimate in the free central limit theorem
Published 30 Mar 2025 in math.PR and math.OA | (2503.23403v1)
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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