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arXiv · 2202.02240

Superconvergence in free probability limit theorems for arbitrary triangular arrays

Hari Bercovici·Ching-Wei Ho·Jiun-Chau Wang·Ping Zhong
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Abstract

It is known that limit theorems for triangular arrays with identically distributed rows yields convergence of densities rather than just convergence in distribution. We show that this superconvergence result holds -- at least at points at which the limit density is nonzero -- even if the rows of the array are not identically distributed.

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Hari Bercovici, Ching-Wei Ho, Jiun-Chau Wang, Ping Zhong. 2022-02-04. Superconvergence in free probability limit theorems for arbitrary triangular arrays. https://arxiv.org/abs/2202.02240

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