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The Normal distribution is freely self-decomposable
| Title: | The Normal distribution is freely self-decomposable |
| Authors: | Hasebe, Takahiro Browse this author →KAKEN DB | | Sakuma, Noriyoshi Browse this author | | Thorbjornsen, Steen Browse this author |
| Issue Date: | Mar-2019 |
| Publisher: | Oxford University Press |
| Journal Title: | IMRN: International Mathematics Research Notices |
| Volume: | 2019 |
| Issue: | 6 |
| Start Page: | 1758 |
| End Page: | 1787 |
| Publisher DOI: | 10.1093/imrn/rnx171 |
| Abstract: | The class of self-decomposable distributions in free probability theory was introduced by Barndorff-Nielsen and Thorbjornsen. It constitutes a fairly large subclass of the freely infinitely divisible distributions, but so far specific examples have been limited to Wigner's semicircle distributions, the free stable distributions, two kinds of free gamma distributions and a few other examples. In this article, we prove that the (classical) normal distributions are freely self-decomposable. More generally it is established that the Askey-Wimp-Kerov distribution mu(c) is freely self-decomposable for any c in [-1, 0]. The main ingredient in the proof is a general characterization of the freely self-decomposable distributions in terms of the derivative of their free cumulant transform. |
| Rights: | This is a pre-copyedited, author-produced version of an article accepted for publication in IMRN: International Mathematics Research Notices following peer review. The version of record The Normal Distribution Is Freely Self-decomposable is available online at: https://academic.oup.com/imrn/article/2019/6/1758/4080658 and 10.1093/imrn/rnx171. |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/76833 |
| 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)
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Submitter: 長谷部 高広
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