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Invariant β-Wishart ensembles, crossover densities and asymptotic corrections to the Marcenko–Pastur law

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorAllez, Romain*
hal.structure.identifierScience & Finance
dc.contributor.authorBouchaud, Jean-Philippe*
hal.structure.identifierLaboratoire de Physique Théorique et Modèles Statistiques [LPTMS]
dc.contributor.authorNajumdar, Satya N.*
hal.structure.identifierLaboratoire de Physique Théorique et Modèles Statistiques [LPTMS]
dc.contributor.authorVivo, Pierpaolo*
dc.date.accessioned2013-01-29T13:58:27Z
dc.date.available2013-01-29T13:58:27Z
dc.date.issued2013
dc.identifier.issn1751-8113
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/10913
dc.language.isoenen
dc.subjectStatistical Mechanics
dc.subjectProbability
dc.subjectmarchenko-Pastur law
dc.subjectβ-Wishart ensemble
dc.subject.ddc519en
dc.titleInvariant β-Wishart ensembles, crossover densities and asymptotic corrections to the Marcenko–Pastur law
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe construct a diffusive matrix model for the β-Wishart (or Laguerre) ensemble for general continuous β ∈ [0, 2], which preserves invariance under the orthogonal/unitary group transformation. Scaling the Dyson index β with the largest size M of the data matrix as β = 2c/M (with c a fixed positive constant), we obtain a family of spectral densities parametrized by c. As c is varied, this density interpolates continuously between the Marčenko–Pastur (c → ∞ limit) and the Gamma law (c → 0 limit). Analyzing the full Stieltjes transform (resolvent) equation, we obtain as a byproduct the correction to the Marčenko–Pastur density in the bulk up to order 1/M for all β and up to order 1/M2 for the particular cases β = 1, 2.
dc.relation.isversionofjnlnameJournal of Physics. A, Mathematical and Theoretical
dc.relation.isversionofjnlvol46
dc.relation.isversionofjnlissue1
dc.relation.isversionofjnldate2013
dc.relation.isversionofdoihttp://dx.doi.org/10.1088/1751-8113/46/1/015001
dc.relation.isversionofjnlpublisherIOP Publishing
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2018-01-22T10:54:52Z
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hal.author.functionaut
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