Electronic Communications in Probability

Free Generalized Gamma Convolutions

Victor Perez Abreu and Noriyoshi Sakuma

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465233477

Digital Object Identifier
doi:10.1214/ECP.v13-1413

Mathematical Reviews number (MathSciNet)
MR2447839

Zentralblatt MATH identifier
1188.15030

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

Keywords
Free probability infinitely divisible distribution generalized gamma convolutions random matrices

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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