Electronic Communications in Probability

Free Generalized Gamma Convolutions

Victor Perez Abreu and Noriyoshi Sakuma

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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.

Article information

Electron. Commun. Probab., Volume 13 (2008), paper no. 50, 526-539.

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 15A52
Secondary: 46L54: Free probability and free operator algebras 60E07: Infinitely divisible distributions; stable distributions

Free probability infinitely divisible distribution generalized gamma convolutions random matrices

This work is licensed under aCreative Commons Attribution 3.0 License.


Perez Abreu, Victor; Sakuma, Noriyoshi. Free Generalized Gamma Convolutions. Electron. Commun. Probab. 13 (2008), paper no. 50, 526--539. doi:10.1214/ECP.v13-1413. https://projecteuclid.org/euclid.ecp/1465233477

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