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Faster Convergence in the Free Central Limit Theorem

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Abstract

We show that there is a faster convergence in the free central limit theorem for measures of bounded support when we have vanishing free cumulants. We give estimates for the extremes of the support and the density of the converging measure. As a consequence, we obtain a more precise Berry–Esseen type estimate than previous results.

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Acknowledgements

The author appreciates the support of CONACYT through the program “Estancias posdoctorales por México”. The author also express sincere thanks to Octavio Arizmendi for useful discussions.

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  1. Instituto de Física, UASLP, San Luis Potosí, México

    Mauricio Salazar

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  1. Mauricio Salazar
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Correspondence to Mauricio Salazar.

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Communicated by Ilwoo Cho.

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Salazar, M. Faster Convergence in the Free Central Limit Theorem. Complex Anal. Oper. Theory 17, 66 (2023). https://doi.org/10.1007/s11785-023-01373-5

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