open access

https://hdl.handle.net/2115/76833

The Normal distribution is freely self-decomposable

英語

2019-03

Oxford University Press

IMRN: International Mathematics Research Notices

2019(6)

1758-1787

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.

学術雑誌論文

Accepted Manuscript

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.

1073-7928

1687-0247