Superconvergence in free probability limit theorems for arbitrary triangular arrays

Bercovici, Hari; Ho, Ching-Wei; Wang, Jiun-Chau; Zhong, Ping

doi:10.1090/proc/16033

Superconvergence in free probability limit theorems for arbitrary triangular arrays
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by Hari Bercovici, Ching-Wei Ho, Jiun-Chau Wang and Ping Zhong PDF

Proc. Amer. Math. Soc. 150 (2022), 5253-5265 Request permission

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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