Classical and free infinitely divisible distributions and random matrices

DOI10.1214/009117904000000982zbMath1076.15022arXivmath/0406082OpenAlexW3100273361MaRDI QIDQ1781178

Florent Benaych-Georges

Publication date: 23 June 2005

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0406082

zbMATH Keywords

free convolutionrandom matricesinfinitely divisible distributionsfree probabilityasymptotic freenessMarchenko-Pastur distribution

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Central limit and other weak theorems (60F05) Free probability and free operator algebras (46L54) Random matrices (algebraic aspects) (15B52)

Related Items (15)

Stochastic Integral and Covariation Representations for Rectangular Lévy Process Ensembles ⋮ Matricial model for the free multiplicative convolution ⋮ Infinitely divisible distributions for rectangular free convolution: classification and matricial interpretation ⋮ Some properties of the free stable distributions ⋮ Lévy-Khintchine random matrices and the Poisson weighted infinite skeleton tree ⋮ On the Hausdorff continuity of free Lévy processes and free convolution semigroups ⋮ On the Process of the Eigenvalues of a Hermitian Lévy process ⋮ Stochastic aspects of easy quantum groups ⋮ Random matrix models of stochastic integral type for free infinitely divisible distributions ⋮ A UNIVERSALITY RESULT FOR THE GLOBAL FLUCTUATIONS OF THE EIGENVECTORS OF WIGNER MATRICES ⋮ Limit theorems for free Lévy processes ⋮ A matrix interpolation between classical and free max operations. I: The univariate case ⋮ On a class of free Lévy laws related to a regression problem ⋮ Liberation of orthogonal Lie groups ⋮ Meixner matrix ensembles

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Self-decomposability and Lévy processes in free probability
• Limit laws for random matrices and free products
• Stable laws and domains of attraction in free probability theory
• Multiplicative functions on the lattice of non-crossing partitions and free convolution
• Brown's spectral distribution measure for \(R\)-diagonal elements in finite von Neumann algebras
• A CONNECTION BETWEEN FREE AND CLASSICAL INFINITE DIVISIBILITY
• On the law of addition of random matrices.
• Partition-dependent stochastic measures and \(q\)-deformed cumulants

This page was built for publication: Classical and free infinitely divisible distributions and random matrices