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Large permutation invariant random matrices are asymptotically free over the diagonal

hal.structure.identifierDepartment of Mathematics [Univ California Davis] [MATH - UC Davis]
dc.contributor.authorAU, Benson
hal.structure.identifierInstitut de Mathématiques de Toulouse UMR5219 [IMT]
dc.contributor.authorCÉBRON, Guillaume
hal.structure.identifierUniversity College Dublin [Dublin] [UCD]
dc.contributor.authorDAHLQVIST, Antoine
hal.structure.identifierDepartment of Mathematics [Imperial College London]
dc.contributor.authorGABRIEL, Franck
hal.structure.identifierCentre National de la Recherche Scientifique [CNRS]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMALE, Camille
dc.date2020
dc.date.accessioned2024-04-04T03:05:36Z
dc.date.available2024-04-04T03:05:36Z
dc.date.issued2020
dc.identifier.issn0091-1798
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193260
dc.description.abstractEnWe prove that independent families of permutation invariant random matrices are asymptotically free over the diagonal, both in probability and in expectation, under a uniform boundedness assumption on the operator norm. We can relax the operator norm assumption to an estimate on sums associated to graphs of matrices, further extending the range of applications (for example, to Wigner matrices with exploding moments and so the sparse regime of the Erdős-Rényi model). The result still holds even if the matrices are multiplied entrywise by bounded random variables (for example, as in the case of matrices with a variance profile and percolation models).
dc.language.isoen
dc.publisherInstitute of Mathematical Statistics
dc.title.enLarge permutation invariant random matrices are asymptotically free over the diagonal
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.subject.halMathématiques [math]/Algèbres d'opérateurs [math.OA]
dc.identifier.arxiv1805.07045
bordeaux.journalAnnals of Probability
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01824543
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01824543v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Annals%20of%20Probability&rft.date=2020&rft.eissn=0091-1798&rft.issn=0091-1798&rft.au=AU,%20Benson&C%C3%89BRON,%20Guillaume&DAHLQVIST,%20Antoine&GABRIEL,%20Franck&MALE,%20Camille&rft.genre=article


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