Free Bessel laws

Details Free Bessel laws Free Bessel laws

2007-10-31

arxiv.org/abs/0710.5931v2

Canad. J. Math. 63 (2011), 3-37

Mathematics

Probability

40 pages

Scientific paper

We introduce and study a remarkable family of real probability measures $\pi_{st}$, that we call free Bessel laws. These are related to the free Poisson law $\pi$ via the formulae $\pi_{s1}=\pi^{\boxtimes s}$ and $\pi_{1t}=\pi^{\boxplus t}$. 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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