Free Bessel Laws

Banica, T. ; Belinschi, S. T. ; Capitaine, M. ; Collins, B.

Canadian journal of mathematics, Tome 63 (2011) no. 1, pp. 3-37

Résumé

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 ${{\text{ }\!\!\pi\!\!\text{ }}_{s1}}={{\text{ }\!\!\pi\!\!\text{ }}^{\boxtimes s}}$ and $\text{ }\pi {{\text{ }}_{1t}}=\text{ }\pi {{\text{ }}^{\boxtimes }}^{t}$ . 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.

Détail

DOI : 10.4153/CJM-2010-060-6

Mots-clés : 46L54, 15A52, 16W30, Poisson law, Bessel function, Wishart matrix, quantum group

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