Superconvergence in free probability limit theorems for arbitrary triangular arrays
Probability
2022-02-07 v1 Functional Analysis
Operator Algebras
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.
Cite
@article{arxiv.2202.02240,
title = {Superconvergence in free probability limit theorems for arbitrary triangular arrays},
author = {Hari Bercovici and Ching-Wei Ho and Jiun-Chau Wang and Ping Zhong},
journal= {arXiv preprint arXiv:2202.02240},
year = {2022}
}