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dc.contributor.authorSchlein, Benjamin
dc.contributor.authorYau, Horng-Tzer
dc.contributor.authorYin, Jun
dc.date.accessioned2016-02-17T21:32:42Z
dc.date.issued2012
dc.identifier.citationErdos, László, Benjamin Schlein, Horng-Tzer Yau, and Jun Yin. 2012. “The Local Relaxation Flow Approach to Universality of the Local Statistics for Random Matrices.” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 48 (1) (February): 1–46. doi:10.1214/10-aihp388.en_US
dc.identifier.issn0246-0203en_US
dc.identifier.urihttp://nrs.harvard.edu/urn-3:HUL.InstRepos:25426537
dc.description.abstractWe present a generalization of the method of the local relaxation flow to establish the universality of local spectral statistics of a broad class of large random matrices. We show that the local distribution of the eigenvalues coincides with the local statistics of the corresponding Gaussian ensemble provided the distribution of the individual matrix element is smooth and the eigenvalues {\(x_{j}\)}\(_{j=1}^{N}\) are close to their classical location {\(\gamma\)\(_{j}\)}\(_{j=1}^{N}\) determined by the limiting density of eigenvalues. Under the scaling where the typical distance between neighboring eigenvalues is of order 1/\(N\), the necessary apriori estimate on the location of eigenvalues requires only to know that \(\mathbb{E}\) |\(x_{j}\) \(-\) \(\gamma\)\(_{j}\)|\(^{2}\) \(\leq\) \(N\)\(^{-1-\epsilon}\) on average. This information can be obtained by well established methods for various matrix ensembles. We demonstrate the method by proving local spectral universality for Wishart matrices.en_US
dc.description.sponsorshipMathematicsen_US
dc.language.isoen_USen_US
dc.publisherInstitute of Mathematical Statisticsen_US
dc.relation.isversionofdoi://10.1214/10-AIHP388en_US
dc.relation.hasversionhttp://arxiv.org/abs/0911.3687v5en_US
dash.licenseOAP
dc.subjectrandom matrixen_US
dc.subjectsample covariance matrixen_US
dc.subjectWishart matrixen_US
dc.subjectWigner–Dyson statisticsen_US
dc.titleThe local relaxation flow approach to universality of the local statistics for random matricesen_US
dc.typeJournal Articleen_US
dc.description.versionAccepted Manuscripten_US
dc.relation.journalAnn. Inst. H. Poincaré Probab. Statist.en_US
dash.depositing.authorYau, Horng-Tzer
dc.date.available2016-02-17T21:32:42Z
dc.identifier.doi10.1214/10-AIHP388*
dash.contributor.affiliatedYau, Horng-Tzer


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