--- _id: '1010' abstract: - lang: eng text: '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∗. ' article_number: '25' article_processing_charge: No author: - first_name: Johannes full_name: Alt, Johannes id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87 last_name: Alt - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Torben H full_name: Krüger, Torben H id: 3020C786-F248-11E8-B48F-1D18A9856A87 last_name: Krüger orcid: 0000-0002-4821-3297 citation: ama: Alt J, Erdös L, Krüger TH. Local law for random Gram matrices. Electronic Journal of Probability. 2017;22. doi:10.1214/17-EJP42 apa: Alt, J., Erdös, L., & Krüger, T. H. (2017). Local law for random Gram matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/17-EJP42 chicago: Alt, Johannes, László Erdös, and Torben H Krüger. “Local Law for Random Gram Matrices.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/17-EJP42. ieee: J. Alt, L. Erdös, and T. H. Krüger, “Local law for random Gram matrices,” Electronic Journal of Probability, vol. 22. Institute of Mathematical Statistics, 2017. ista: Alt J, Erdös L, Krüger TH. 2017. Local law for random Gram matrices. Electronic Journal of Probability. 22, 25. mla: Alt, Johannes, et al. “Local Law for Random Gram Matrices.” Electronic Journal of Probability, vol. 22, 25, Institute of Mathematical Statistics, 2017, doi:10.1214/17-EJP42. short: J. Alt, L. Erdös, T.H. Krüger, Electronic Journal of Probability 22 (2017). date_created: 2018-12-11T11:49:40Z date_published: 2017-03-08T00:00:00Z date_updated: 2023-09-22T09:45:23Z day: '08' ddc: - '510' - '539' department: - _id: LaEr doi: 10.1214/17-EJP42 ec_funded: 1 external_id: arxiv: - '1606.07353' isi: - '000396611900025' file: - access_level: open_access content_type: application/pdf creator: system date_created: 2018-12-12T10:13:39Z date_updated: 2018-12-12T10:13:39Z file_id: '5024' file_name: IST-2017-807-v1+1_euclid.ejp.1488942016.pdf file_size: 639384 relation: main_file file_date_updated: 2018-12-12T10:13:39Z has_accepted_license: '1' intvolume: ' 22' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Published Version project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Electronic Journal of Probability publication_identifier: issn: - '10836489' publication_status: published publisher: Institute of Mathematical Statistics publist_id: '6386' pubrep_id: '807' quality_controlled: '1' related_material: record: - id: '149' relation: dissertation_contains status: public scopus_import: '1' status: public title: Local law for random Gram matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 22 year: '2017' ...