A Khintchine Decomposition for Free Probability

Details A Khintchine Decomposition for Free Probability A Khintchine Decomposition for Free Probability

2010-09-24

arxiv.org/abs/1009.4955v2

Mathematics

Operator Algebras

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Scientific paper

Let $\mu$ be a probability measure on the real line. In this paper we prove that there exists a decomposition $\mu = \mu_{0} \boxplus \mu_{1} \boxplus \... \boxplus \mu_{n} \boxplus \...$ such that $\mu_{0}$ is infinitely divisible and $\mu_{i}$ is indecomposable for $i \geq 1$. 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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