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January 2008 Limit theorems in free probability theory. I
G. P. Chistyakov, F. Götze
Ann. Probab. 36(1): 54-90 (January 2008). DOI: 10.1214/009117907000000051


Based on an analytical approach to the definition of additive free convolution on probability measures on the real line, we prove free analogues of limit theorems for sums for nonidentically distributed random variables in classical probability theory.


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G. P. Chistyakov. F. Götze. "Limit theorems in free probability theory. I." Ann. Probab. 36 (1) 54 - 90, January 2008.


Published: January 2008
First available in Project Euclid: 28 November 2007

zbMATH: 1157.46037
MathSciNet: MR2370598
Digital Object Identifier: 10.1214/009117907000000051

Primary: 46L50 , 60E07
Secondary: 60E10

Keywords: Cauchy transforms , free convolutions , free random variables , limit theorems

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.36 • No. 1 • January 2008
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