dc.contributor.author | Alex, Bloemendal | |
dc.contributor.author | Erdos, Laszlo | |
dc.contributor.author | Knowles, Antti | |
dc.contributor.author | Yau, Horng-Tzer | |
dc.contributor.author | Yin, Jun | |
dc.date.accessioned | 2017-10-18T15:50:31Z | |
dc.date.issued | 2014 | |
dc.identifier.citation | Alex, Bloemendal, László Erdős, Antti Knowles, Horng-Tzer Yau, and Jun Yin. 2014. “Isotropic Local Laws for Sample Covariance and Generalized Wigner Matrices.” Electronic Journal of Probability 19 (0). doi:10.1214/ejp.v19-3054. | en_US |
dc.identifier.issn | 1083-6489 | en_US |
dc.identifier.uri | http://nrs.harvard.edu/urn-3:HUL.InstRepos:34253795 | |
dc.description.abstract | We consider sample covariance matrices of the form X ∗X, where X is an M × N matrix with independent random entries. We prove the isotropic local MarchenkoPastur law, i.e. we prove that the resolvent (X ∗X − z) −1 converges to a multiple of the identity in the sense of quadratic forms. More precisely, we establish sharp high-probability bounds on the quantity hv,(X ∗X − z) −1wi − hv, wim(z), where m is the Stieltjes transform of the Marchenko-Pastur law and v, w ∈ C N . We require the logarithms of the dimensions M and N to be comparable. Our result holds down to scales Im z > N −1+ε and throughout the entire spectrum away from 0. We also prove analogous results for generalized Wigner matrices. | en_US |
dc.description.sponsorship | Mathematics | en_US |
dc.language.iso | en_US | en_US |
dc.publisher | Institute of Mathematical Statistics | en_US |
dc.relation.isversionof | doi:10.1214/EJP.v19-3054 | en_US |
dash.license | LAA | |
dc.subject | Sample covariance matrix | en_US |
dc.subject | isotropic local law | en_US |
dc.subject | eigenvalue rigidity | en_US |
dc.subject | delocalization | en_US |
dc.title | Isotropic local laws for sample covariance and generalized Wigner matrices | en_US |
dc.type | Journal Article | en_US |
dc.description.version | Version of Record | en_US |
dc.relation.journal | Electronic Journal of Probability | en_US |
dash.depositing.author | Yau, Horng-Tzer | |
dc.date.available | 2017-10-18T15:50:31Z | |
dc.identifier.doi | 10.1214/EJP.v19-3054 | * |
dash.authorsordered | false | |
dash.contributor.affiliated | Yin, Jun | |
dash.contributor.affiliated | Yau, Horng-Tzer | |
dash.contributor.affiliated | Erdos, Laszlo | |