The Normal Distribution Is Freely Self-decomposable
The Normal Distribution Is Freely Self-decomposable
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正态分布可自由自分解
DOI：
10.1093/imrn/rnx171
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发表时间：
2019
影响因子：
1
通讯作者：
Noriyoshi Sakuma and Steen Thorbjornsen
中科院分区：
文献类型：
--
作者：
Takahiro Hasebe; Noriyoshi Sakuma and Steen Thorbjornsen
自由概率论中的自分解分布类是由Barndorff-Nielsen和Thorbj-rnsen引入的。它构成了自由无限可分分布的一个相当大的子类，但到目前为止，具体的例子仅限于维格纳的周期分布，自由稳定分布，两种自由伽马分布和一些其他的例子。在这篇文章中，我们证明了（经典）正态分布是自由自分解的。更一般地说，它是建立Askey-Wimp-Kerov分布是自由自分解的阴。在证明的主要成分是自由自分解分布的自由累积量变换的导数方面的一般特征。
The class of self-decomposable distributions in free probability theory was introduced by Barndorff–Nielsen and Thorbj⊘rnsen. 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 distributionis freely self-decomposable for anyin. 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.