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dc.contributor.authorAdamczak, R.
dc.contributor.authorChafaï, Djalil
dc.contributor.authorWolff, P.
dc.date.accessioned2014-02-26T14:40:03Z
dc.date.available2014-02-26T14:40:03Z
dc.date.issued2016
dc.identifier.issn1042-9832
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/12761
dc.language.isofren
dc.subjectsmallest singular value
dc.subjectspectral analysis
dc.subjectRandom permutations
dc.subjectexchangeable distributions
dc.subjectconcentration of measure
dc.subjectCombinatorial Central Limit Theorem
dc.subjectRandom matrices
dc.subject.ddc519en
dc.titleCircular law for random matrices with exchangeable entries
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherInstitute of Mathematics, Polish Academy of Sciences Polish Academy of Sciences;Pologne
dc.contributor.editoruniversityotherInstitut Universitaire de France (IUF) http://iuf.amue.fr/ Ministère de l'Enseignement Supérieur et de la Recherche Scientifique;France
dc.contributor.editoruniversityotherInstitute of Mathematics, University of Warsaw University of Warsaw;Pologne
dc.description.abstractenAn exchangeable random matrix is a random matrix with distribution invariant under any permutation of the entries. For such random matrices, we show, as the dimension tends to infinity, that the empirical spectral distribution tends to the uniform law on the unit disc. This is an instance of the universality phenomenon known as the circular law, for a model of random matrices with dependent entries, rows, and columns. It is also a non-Hermitian counterpart of a result of Chatterjee on the semi-circular law for random Hermitian matrices with exchangeable entries. The proof relies in particular on a reduction to a simpler model given by a random shuffle of a rigid deterministic matrix, on Hermitization, and also on combinatorial concentration of measure and combinatorial Central Limit Theorem. A crucial step is a polynomial bound on the smallest singular value of exchangeable random matrices, which may be of independent interest.
dc.publisher.cityParisen
dc.relation.isversionofjnlnameRandom Structures & Algorithms
dc.relation.isversionofjnlvol48
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2016
dc.relation.isversionofjnlpages454-479
dc.relation.isversionofdoi10.1002/rsa.20599
dc.identifier.urlsitehttps://arxiv.org/abs/1402.3660v1
dc.relation.isversionofjnlpublisherWiley
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.submittednonen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceNational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2020-05-04T08:45:00Z
hal.person.labIds179410*
hal.person.labIds60*
hal.person.labIds179410*


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