The Annals of Probability

Limit theorems in free probability theory. I

G. P. Chistyakov and F. Götze

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Probab., Volume 36, Number 1 (2008), 54-90.

Dates
First available in Project Euclid: 28 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1196268673

Digital Object Identifier
doi:10.1214/009117907000000051

Mathematical Reviews number (MathSciNet)
MR2370598

Zentralblatt MATH identifier
1157.46037

Subjects
Primary: 46L50 60E07: Infinitely divisible distributions; stable distributions
Secondary: 60E10: Characteristic functions; other transforms

Keywords
Free random variables Cauchy transforms free convolutions limit theorems

Citation

Chistyakov, G. P.; Götze, F. Limit theorems in free probability theory. I. Ann. Probab. 36 (2008), no. 1, 54--90. doi:10.1214/009117907000000051. https://projecteuclid.org/euclid.aop/1196268673


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