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September 2012 A Khintchine decomposition for free probability
John D. Williams
Ann. Probab. 40(5): 2236-2263 (September 2012). DOI: 10.1214/11-AOP677

Abstract

Let $\mu$ be a probability measure on the real line. In this paper we prove that there exists a decomposition $\mu=\mu_{0}\boxplus\mu_{1}\boxplus\cdots\boxplus\mu_{n}\boxplus\cdots$ such that $\mu_{0}$ is infinitely divisible, and $\mu_{i}$ is indecomposable for $i\geq1$. Additionally, we prove that the family of all $\boxplus$-divisors of a measure $\mu$ is compact up to translation. Analogous results are also proven in the case of multiplicative convolution.

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John D. Williams. "A Khintchine decomposition for free probability." Ann. Probab. 40 (5) 2236 - 2263, September 2012. https://doi.org/10.1214/11-AOP677

Information

Published: September 2012
First available in Project Euclid: 8 October 2012

zbMATH: 1260.60185
MathSciNet: MR3025716
Digital Object Identifier: 10.1214/11-AOP677

Subjects:
Primary: 60K35

Keywords: Decomposition , Free probability , Infinite divisibility

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 5 • September 2012
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