The Annals of Probability

Local limit theorems in free probability theory

Jiun-Chau Wang

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Abstract

In this paper, we study the superconvergence phenomenon in the free central limit theorem for identically distributed, unbounded summands. We prove not only the uniform convergence of the densities to the semicircular density but also their Lp-convergence to the same limit for p > 1/2. Moreover, an entropic central limit theorem is obtained as a consequence of the above results.

Article information

Source
Ann. Probab., Volume 38, Number 4 (2010), 1492-1506.

Dates
First available in Project Euclid: 8 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.aop/1278593957

Digital Object Identifier
doi:10.1214/09-AOP505

Mathematical Reviews number (MathSciNet)
MR2663634

Zentralblatt MATH identifier
1202.46078

Subjects
Primary: 46L54: Free probability and free operator algebras
Secondary: 60F05: Central limit and other weak theorems 60F25: $L^p$-limit theorems

Keywords
Free central limit theorem superconvergence local limit theorems free entropy

Citation

Wang, Jiun-Chau. Local limit theorems in free probability theory. Ann. Probab. 38 (2010), no. 4, 1492--1506. doi:10.1214/09-AOP505. https://projecteuclid.org/euclid.aop/1278593957


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