Infinitely divisible distributions for rectangular free convolution: classification and matricial interpretation

DOI10.1007/s00440-006-0042-1zbMath1129.15019arXivmath/0512080OpenAlexW2094607534MaRDI QIDQ2641902

Florent Benaych-Georges

Publication date: 17 August 2007

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0512080

zbMATH Keywords

free convolutionrandom matricesconvolution operatorfree probabilityMarchenko-Pastur distributionLevy-Khinchine type theorem

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 (8)

Stochastic Integral and Covariation Representations for Rectangular Lévy Process Ensembles ⋮ Rectangular random matrices, related convolution ⋮ The singular values and vectors of low rank perturbations of large rectangular random matrices ⋮ On a surprising relation between the Marchenko-Pastur law, rectangular and square free convolutions ⋮ Rectangular \(R\)-transform as the limit of rectangular spherical integrals ⋮ The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices ⋮ On the asymptotic distribution of block-modified random matrices ⋮ Limit theorems for Bessel and Dunkl processes of large dimensions and free convolutions

Cites Work

• Self-decomposability and Lévy processes in free probability
• A matrix representation of the Bercovici-Pata bijection
• Notes on non-commutative integration
• Stable laws and domains of attraction in free probability theory
• Classical and free infinitely divisible distributions and random matrices
• Rectangular random matrices, related convolution
• Free Random Variables
• Combinatorial theory of the free product with amalgamation and operator-valued free probability theory
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