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.
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