# Indiana University

 dc.contributor.author Williams, J.D. dc.date.accessioned 2014-11-03T19:26:42Z dc.date.available 2014-11-03T19:26:42Z dc.date.issued 2012 dc.identifier.citation Williams, J. D. (2012). A khintchine decomposition for free probability. Annals of Probability, 40(5), 2236-2263. http://dx.doi.org/10.1214/11-AOP677 en dc.identifier.uri http://hdl.handle.net/2022/19106 dc.description.abstract Let μ be a probability measure on the real line. In this paper we prove that there exists a decomposition $\mu = \mu_{0}\boxplus \mu_{1}\dots\boxplus \mu_{n}$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 en dc.language.iso en_US en dc.publisher Institute of Mathematical Statistics en dc.relation.isversionof https://doi.org/10.1214/11-AOP677 en dc.rights © 2012 Institute of Mathematical Statistics en dc.subject Decomposition en dc.subject Free probability en dc.subject Infinite divisibility en dc.title A khintchine decomposition for free probability en dc.type Article en dc.altmetrics.display false en
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