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dc.contributor.authorBourgade, Paul
dc.contributor.authorYau, Horng-Tzer
dc.contributor.authorYin, Jun
dc.date.accessioned2017-05-18T18:49:51Z
dc.date.issued2013
dc.identifier.citationBourgade, Paul, Horng-Tzer Yau, and Jun Yin. 2013. “The Local Circular Law II: The Edge Case.” Probability Theory and Related Fields 159 (3-4) (July 16): 619–660. doi:10.1007/s00440-013-0516-x.en_US
dc.identifier.issn0178-8051en_US
dc.identifier.urihttp://nrs.harvard.edu/urn-3:HUL.InstRepos:32706744
dc.description.abstractIn the first part of this article (Bourgade et al. arXiv:1206.1449, 2012), we proved a local version of the circular law up to the finest scale N−1/2+εN−1/2+ε for non-Hermitian random matrices at any point z∈ℂz∈C with ||z|−1|>c||z|−1|>c for any c>0c>0 independent of the size of the matrix. Under the main assumption that the first three moments of the matrix elements match those of a standard Gaussian random variable after proper rescaling, we extend this result to include the edge case |z|−1=o(1)|z|−1=o(1). Without the vanishing third moment assumption, we prove that the circular law is valid near the spectral edge |z|−1=o(1)|z|−1=o(1) up to scale N−1/4+εN−1/4+ε.en_US
dc.description.sponsorshipMathematicsen_US
dc.language.isoen_USen_US
dc.publisherSpringer Natureen_US
dc.relation.isversionofdoi:10.1007/s00440-013-0516-xen_US
dc.relation.hasversionhttps://arxiv.org/abs/1206.3187en_US
dash.licenseOAP
dc.subjectLocal circular lawen_US
dc.subjectuniversalityen_US
dc.titleThe local circular law II: the edge caseen_US
dc.typeJournal Articleen_US
dc.description.versionAccepted Manuscripten_US
dc.relation.journalProbability Theory and Related Fieldsen_US
dash.depositing.authorYau, Horng-Tzer
dc.date.available2017-05-18T18:49:51Z
dc.identifier.doi10.1007/s00440-013-0516-x*
dash.contributor.affiliatedYin, Jun
dash.contributor.affiliatedYau, Horng-Tzer


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