Classical and free infinitely divisible distributions and random matrices

Simple item page
dc.creatorBenaych-Georges, Florent
dc.date2004-06-04
dc.date2005-08-30
dc.date.accessioned2026-07-07T05:08:53Z
dc.date.available2026-07-07T05:08:53Z
dc.descriptionWe construct a random matrix model for the bijection Ψbetween clas- sical and free infinitely divisible distributions: for every d\geq1, we associate in a quite natural way to each *-infinitely divisible distribution μa distribution P_d^μ on the space of d\times d Hermitian matrices such that P_d^μP_d^ν=P_d^{μ*ν}. The spectral distribution of a random matrix with distribution P_d^μ converges in probability to Ψ(μ) when d tends to +\infty. It gives, among other things, a new proof of the almost sure convergence of the spectral distribution of a matrix of the GUE and a projection model for the Marchenko-Pastur distribution. In an analogous way, for every d\geq1, we associate to each *-infinitely divisible distribution μ, a distribution L_d^μ on the space of complex (non-Hermitian) d\times d random matrices. If μis symmetric, the symmetrization of the spectral distribution of |M_d|, when M_d is L_d^μ-distributed, converges in probability to Ψ(μ).
dc.descriptionPublished at http://dx.doi.org/10.1214/009117904000000982 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0406082
dc.identifierhttp://arxiv.org/abs/math/0406082
dc.identifierAnnals of Probability 2005, Vol. 33, No. 3, 1134-1170
dc.identifierdoi:10.1214/009117904000000982
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71438
dc.subjectProbability
dc.subjectOperator Algebras
dc.subject15A52, 46L54 (Primary) 60E07, 60F05. (Secondary)
dc.titleClassical and free infinitely divisible distributions and random matrices
dc.typetext

Files

Collections

arXiv