Abstract view
Published:20100706
Printed: Feb 2011
T. Banica,
Department of Mathematics, Toulouse 3 University, Toulouse, France
S. T. Belinschi,
Department of Mathematics, University of Saskatchewan, Saskatoon, SK
M. Capitaine,
Department of Mathematics, Toulouse 3 University, Toulouse, France
B. Collins,
Department of Mathematics, Lyon 1 University, France
Abstract
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.
MSC Classifications: 
46L54, 15A52, 16W30 show english descriptions
Free probability and free operator algebras Random matrices Coalgebras, bialgebras, Hopf algebras (See also 16S40, 57T05); rings, modules, etc. on which these act
46L54  Free probability and free operator algebras 15A52  Random matrices 16W30  Coalgebras, bialgebras, Hopf algebras (See also 16S40, 57T05); rings, modules, etc. on which these act
