Free self-decomposability and unimodality of the Fuss-Catalan distributions

Wojciech Młotkowski; Noriyoshi Sakuma; Yuki Ueda

doi:10.1007/s10955-020-02488-1

Free self-decomposability and unimodality of the Fuss-Catalan distributions

Probability 2022-09-05 v1 Combinatorics

Authors: Wojciech Młotkowski , Noriyoshi Sakuma , Yuki Ueda

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Abstract

We study properties of the Fuss-Catalan distributions $\mu(p,r)$ , $p\geq1$ , $0<r\leq p$ : free infinite divisibility, free self-decomposability, free regularity and unimodality. We show that the Fuss-Catalan distribution $\mu(p,r)$ is freely self-decomposable if and only if $1 \leq p=r \leq 2$ .

Keywords

Fuss-Catalan distributions free self-decomposability free infinite divisibility unimodality free regularity free probability

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@article{arxiv.1908.07887,
  title  = {Free self-decomposability and unimodality of the Fuss-Catalan distributions},
  author = {Wojciech Młotkowski and Noriyoshi Sakuma and Yuki Ueda},
  journal= {arXiv preprint arXiv:1908.07887},
  year   = {2022}
}

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16 pages, 2 figures

Free self-decomposability and unimodality of the Fuss-Catalan distributions

Abstract

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