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arXiv · 2111.10150

Probability distributions with rational free $R$-transform

Wojciech Młotkowski
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Abstract

We study the class $\mathcal{M}_{\mathrm{ratio}}$ of those probability distributions for which the free $R$-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 $R$-transform of a probability distribution. Several examples are provided, including that of free deconvolution.

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Wojciech Młotkowski. 2021-11-19. Probability distributions with rational free $R$-transform. https://arxiv.org/abs/2111.10150

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