Free Bessel laws
Abstract
We introduce and study a remarkable family of real probability measures πst, that we call free Bessel laws. These are related to the free Poisson law π via the formulae πs1=π s and π1t=π 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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