Open Access
2008 Free Generalized Gamma Convolutions
Victor Perez Abreu, Noriyoshi Sakuma
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Electron. Commun. Probab. 13: 526-539 (2008). DOI: 10.1214/ECP.v13-1413


The so-called Bercovici-Pata bijection maps the set of classical infinitely divisible laws to the set of free infinitely divisible laws. The purpose of this work is to study the free infinitely divisible laws corresponding to the classical Generalized Gamma Convolutions (GGC). Characterizations of their free cumulant transforms are derived as well as free integral representations with respect to the free Gamma process. A random matrix model for free GGC is built consisting of matrix random integrals with respect to a classical matrix Gamma process. Nested subclasses of free GGC are shown to converge to the free stable class of distributions.


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Victor Perez Abreu. Noriyoshi Sakuma. "Free Generalized Gamma Convolutions." Electron. Commun. Probab. 13 526 - 539, 2008.


Accepted: 14 October 2008; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1188.15030
MathSciNet: MR2447839
Digital Object Identifier: 10.1214/ECP.v13-1413

Primary: 15A52
Secondary: 46L54 , 60E07

Keywords: Free probability , Generalized gamma convolutions , infinitely divisible distribution , random matrices

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