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Free Bessel Laws

  • T. Banica (a1), S. T. Belinschi (a2), M. Capitaine (a1) and B. Collins (a3)

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 ⊠s and π1tt . 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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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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