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July 2010 Local limit theorems in free probability theory
Jiun-Chau Wang
Ann. Probab. 38(4): 1492-1506 (July 2010). DOI: 10.1214/09-AOP505


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.


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Jiun-Chau Wang. "Local limit theorems in free probability theory." Ann. Probab. 38 (4) 1492 - 1506, July 2010.


Published: July 2010
First available in Project Euclid: 8 July 2010

zbMATH: 1202.46078
MathSciNet: MR2663634
Digital Object Identifier: 10.1214/09-AOP505

Primary: 46L54
Secondary: 60F05 , 60F25

Keywords: Free central limit theorem , Free entropy , Local limit theorems , superconvergence

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 4 • July 2010
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