Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 13 (2008), paper no. 50, 526-539.
Free Generalized Gamma Convolutions
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.
Electron. Commun. Probab., Volume 13 (2008), paper no. 50, 526-539.
Accepted: 14 October 2008
First available in Project Euclid: 6 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Secondary: 46L54: Free probability and free operator algebras 60E07: Infinitely divisible distributions; stable distributions
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