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dc.contributor.authorBordenave, Charles*
dc.contributor.authorCaputo, Pietro*
dc.contributor.authorChafaï, Djalil*
dc.contributor.authorTikhomirov, Konstantin*
dc.date.accessioned2017-11-29T14:46:31Z
dc.date.available2017-11-29T14:46:31Z
dc.date.issued2018
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17108
dc.language.isoenen
dc.subjectCombinatorics
dc.subjectDigraph
dc.subjectSpectral Radius
dc.subjectRandom matrix
dc.subjectHeavy Tail
dc.subject.ddc519en
dc.titleOn the spectral radius of a random matrix: An upper bound without fourth moment
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenConsider a square matrix with independent and identically distributed entries of zero mean and unit variance. It is well known that if the entries have a finite fourth moment, then, in high dimension, with high probability, the spectral radius is close to the square root of the dimension. We conjecture that this holds true under the sole assumption of zero mean and unit variance, in other words that there are no outliers in the circular law. In this work we establish the conjecture in the case of symmetrically distributed entries with a finite moment of order larger than two. The proof uses the method of moments combined with a novel truncation technique for cycle weights that might be of independent interest.
dc.relation.isversionofjnlnameAnnals of Probability
dc.relation.isversionofjnlvol46
dc.relation.isversionofjnlissue4
dc.relation.isversionofjnldate2018
dc.relation.isversionofjnlpages2268-2286
dc.relation.isversionofdoi10.1214/17-AOP1228
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01346261
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.ssrncandidatenon
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dc.description.readershiprecherche
dc.description.audienceInternational
dc.date.updated2017-12-19T16:41:58Z
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