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 Electronic Communications in Probability > Vol. 13 (2008) > Paper 50 open journal systems 


Free Generalized Gamma Convolutions

Victor Perez Abreu, CIMAT
Noriyoshi Sakuma, Keio University


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.


Full text: PDF

Pages: 526-539

Published on: October 14, 2008
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Electronic Communications in Probability. ISSN: 1083-589X