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On Free Generalized Inverse Gaussian Distributions

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Title: On Free Generalized Inverse Gaussian Distributions
Authors: Hasebe, Takahiro Browse this author →KAKEN DB
Szpojankowski, Kamil Browse this author
Issue Date: Oct-2019
Journal Title: Complex Analysis and Operator Theory
Volume: 13
Issue: 7
Start Page: 3091
End Page: 3116
Publisher DOI: 10.1007/s11785-018-0790-9
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 X, Y where Y has a free Poisson distribution one has $X\triangleq\frac{1}{X+Y}$ if and only if X 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.
Rights: This is a post-peer-review, pre-copyedit version of an article published in Complex analysis and operator theory. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11785-018-0790-9.
Type: article
URI: http://hdl.handle.net/2115/75996
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 長谷部 高広

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