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arXiv · 1302.3738

On the free Gamma distributions

Uffe Haagerup·Steen Thorbjornsen
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Abstract

For each positive number $\alpha$ we study the analog $\nu_alpha$ in free probability of the classical Gamma distribution with parameter $\alpha$. We prove that $\nu_\alpha$ is absolutely continuous and establish the main properties of the density, including analyticity and unimodality. We study further the asymptotic behavior of $\nu_\alpha$ as $\alpha\downarrow0$.

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Uffe Haagerup, Steen Thorbjornsen. 2013-02-15. On the free Gamma distributions. https://arxiv.org/abs/1302.3738

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