--- res: bibo_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 Marchenko-Pastur 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 ⟨v,(X∗X−z)−1w⟩−⟨v,w⟩m(z), where m is the Stieltjes transform of the Marchenko-Pastur law and v,w∈CN. We require the logarithms of the dimensions M and N to be comparable. Our result holds down to scales Iz≥N−1+ε and throughout the entire spectrum away from 0. We also prove analogous results for generalized Wigner matrices.\r\n@eng" bibo_authorlist: - foaf_Person: foaf_givenName: Alex foaf_name: Bloemendal, Alex foaf_surname: Bloemendal - foaf_Person: foaf_givenName: László foaf_name: Erdös, László foaf_surname: Erdös foaf_workInfoHomepage: http://www.librecat.org/personId=4DBD5372-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0001-5366-9603 - foaf_Person: foaf_givenName: Antti foaf_name: Knowles, Antti foaf_surname: Knowles - foaf_Person: foaf_givenName: Horng foaf_name: Yau, Horng foaf_surname: Yau - foaf_Person: foaf_givenName: Jun foaf_name: Yin, Jun foaf_surname: Yin bibo_doi: 10.1214/EJP.v19-3054 bibo_volume: 19 dct_date: 2014^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/10836489 dct_language: eng dct_publisher: Institute of Mathematical Statistics@ dct_title: Isotropic local laws for sample covariance and generalized Wigner matrices@ ...