Rectangular \(R\)-transform as the limit of rectangular spherical integrals

DOI10.1007/s10959-011-0362-7zbMath1237.15031arXiv0909.0178OpenAlexW2148136784MaRDI QIDQ662869

Florent Benaych-Georges

Publication date: 13 February 2012

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.0178

zbMATH Keywords

random matricesHaar measurefree probabilityspherical integralslog-Laplace transformrectangular free convolutionrectangular R-transform

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Free probability and free operator algebras (46L54) Laplace transform (44A10) Random matrices (algebraic aspects) (15B52) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (7)

Approximate message passing algorithms for rotationally invariant matrices ⋮ Right large deviation principle for the top eigenvalue of the sum or product of invariant random matrices ⋮ Perturbative construction of mean-field equations in extensive-rank matrix factorization and denoising ⋮ Asymptotics of rectangular spherical integrals ⋮ The singular values and vectors of low rank perturbations of large rectangular random matrices ⋮ Asymptotics of k dimensional spherical integrals and applications ⋮ A dynamical mean-field theory for learning in restricted Boltzmann machines

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