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

Abstract

We study properties of the Fuss-Catalan distributions $\mu (p,r)$, $p\ge 1$, $0<r\le p$: 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 $1\le p=r\le 2$.

arXiv comment16 pages, 2 figures

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