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arXiv · 0710.5931

Free Bessel laws

Teodor Banica·Serban Belinschi·Mireille Capitaine·Benoit Collins
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Abstract

We introduce and study a remarkable family of real probability measures $π_{st}$, that we call free Bessel laws. These are related to the free Poisson law $π$ via the formulae $π_{s1}=π^{\boxtimes s}$ and $π_{1t}=π^{\boxplus t}$. Our study includes: definition and basic properties, analytic aspects (supports, atoms, densities), combinatorial aspects (functional transforms, moments, partitions), and a discussion of the relation with random matrices and quantum groups.

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Teodor Banica, Serban Belinschi, Mireille Capitaine, Benoit Collins. 2008-04-15. Free Bessel laws. https://doi.org/10.4153/cjm-2010-060-6

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