--- res: bibo_abstract: - We prove a local law in the bulk of the spectrum for random Gram matrices XX∗, a generalization of sample covariance matrices, where X is a large matrix with independent, centered entries with arbitrary variances. The limiting eigenvalue density that generalizes the Marchenko-Pastur law is determined by solving a system of nonlinear equations. Our entrywise and averaged local laws are on the optimal scale with the optimal error bounds. They hold both in the square case (hard edge) and in the properly rectangular case (soft edge). In the latter case we also establish a macroscopic gap away from zero in the spectrum of XX∗. @eng bibo_authorlist: - foaf_Person: foaf_givenName: Johannes foaf_name: Alt, Johannes foaf_surname: Alt foaf_workInfoHomepage: http://www.librecat.org/personId=36D3D8B6-F248-11E8-B48F-1D18A9856A87 - 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: Torben H foaf_name: Krüger, Torben H foaf_surname: Krüger foaf_workInfoHomepage: http://www.librecat.org/personId=3020C786-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-4821-3297 bibo_doi: 10.1214/17-EJP42 bibo_volume: 22 dct_date: 2017^xs_gYear dct_identifier: - UT:000396611900025 dct_isPartOf: - http://id.crossref.org/issn/10836489 dct_language: eng dct_publisher: Institute of Mathematical Statistics@ dct_title: Local law for random Gram matrices@ ...