On free Generalized Inverse Gaussian distributions
Operator Algebras
2020-09-24 v1 Probability
Abstract
We study here properties of free Generalized Inverse Gaussian distributions (fGIG) in free probability. We show that in many cases the fGIG shares similar properties with the classical GIG distribution. In particular we prove that fGIG is freely infinitely divisible, free regular and unimodal, and moreover we determine which distributions in this class are freely selfdecomposable. In the second part of the paper we prove that for free random variables where has a free Poisson distribution one has if and only if has fGIG distribution for special choice of parameters. We also point out that the free GIG distribution maximizes the same free entropy functional as the classical GIG does for the classical entropy.
Cite
@article{arxiv.1710.04572,
title = {On free Generalized Inverse Gaussian distributions},
author = {Takahiro Hasebe and Kamil Szpojankowski},
journal= {arXiv preprint arXiv:1710.04572},
year = {2020}
}