Free Bessel Laws

By T. Banica, Serban Teodor Belinschi, M. Capitaine, Benoît Collins. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2007

119 citations recorded by the source corpus.

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

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/94a1d1155198483a4e445a309c5b8b2a92160eff

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Karol Zyczkowski
2. T. Banica
3. Roland Speicher
4. Benoît Collins

In Statistics and Probability

1. Roland Speicher
2. T. Banica
3. Benoît Collins
4. Stephen J. Curran
5. Ion Nechita
6. Karol A. Penson
7. Karol Zyczkowski
8. Moritz Weber

Citations in the corpus

• Generating random density matrices (2010, background): “Armstrong, Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups MWMO 949 (Providence RI: AMS Bookstore, 2009) [11] T.”
• Classification results for easy quantum groups (2009, methodology): “For the top left set, this follows either from the results in [Banica et al. 2007a; Banica and Vergnioux 2009a] regarding the free version H s+ n , after adding a crossing, or from the s =∞ computation in the proof of Theorem 2.”