Probability distributions with rational free $R$-transform
Probability
2021-11-22 v1 Combinatorics
Abstract
We study the class of those probability distributions for which the free -transforms are rational functions. This class is closed under the additive free convolution, additive free powers and under the monotone convolution. We prove a sufficient condition that a rational function is the free -transform of a probability distribution. Several examples are provided, including that of free deconvolution.
Cite
@article{arxiv.2111.10150,
title = {Probability distributions with rational free $R$-transform},
author = {Wojciech Młotkowski},
journal= {arXiv preprint arXiv:2111.10150},
year = {2021}
}