arXiv subjects

Mireille Capitaine

Publications and source records attributed to Mireille Capitaine.

20 records · Page 2Linked to original sources

arXiv2008

Free Bessel laws

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 $π_{s1}=π^{\boxtimes s}$ and $π_{1t}=π^{\boxplus t}$. 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.

math.PR↗

arXiv2005

Strong asymptotic freeness for Wigner and Wishart matrices

We prove that any non commutative polynomial of r independent copies of Wigner matrices converges a.s. towards the polynomial of r free semicircular variables in operator norm. This result extends a previous work of Haagerup and Thorbjornsen where GUE matrices are considered, as well as the classical asymptotic freeness for Wigner matrices (i.e. convergence of the moments) proved by Dykema. We also study the Wishart case.

math.PR↗