{"date_published":"2017-03-08T00:00:00Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"08","ec_funded":1,"publisher":"Institute of Mathematical Statistics","year":"2017","oa_version":"Published Version","title":"Local law for random Gram matrices","scopus_import":"1","quality_controlled":"1","language":[{"iso":"eng"}],"pubrep_id":"807","intvolume":"        22","file":[{"date_created":"2018-12-12T10:13:39Z","access_level":"open_access","file_name":"IST-2017-807-v1+1_euclid.ejp.1488942016.pdf","relation":"main_file","creator":"system","file_id":"5024","date_updated":"2018-12-12T10:13:39Z","content_type":"application/pdf","file_size":639384}],"publist_id":"6386","file_date_updated":"2018-12-12T10:13:39Z","oa":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","ddc":["510","539"],"external_id":{"isi":["000396611900025"],"arxiv":["1606.07353"]},"status":"public","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"}],"date_created":"2018-12-11T11:49:40Z","month":"03","citation":{"chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “Local Law for Random Gram Matrices.” <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics, 2017. <a href=\"https://doi.org/10.1214/17-EJP42\">https://doi.org/10.1214/17-EJP42</a>.","ista":"Alt J, Erdös L, Krüger TH. 2017. Local law for random Gram matrices. Electronic Journal of Probability. 22, 25.","apa":"Alt, J., Erdös, L., &#38; Krüger, T. H. (2017). Local law for random Gram matrices. <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/17-EJP42\">https://doi.org/10.1214/17-EJP42</a>","short":"J. Alt, L. Erdös, T.H. Krüger, Electronic Journal of Probability 22 (2017).","ama":"Alt J, Erdös L, Krüger TH. Local law for random Gram matrices. <i>Electronic Journal of Probability</i>. 2017;22. doi:<a href=\"https://doi.org/10.1214/17-EJP42\">10.1214/17-EJP42</a>","mla":"Alt, Johannes, et al. “Local Law for Random Gram Matrices.” <i>Electronic Journal of Probability</i>, vol. 22, 25, Institute of Mathematical Statistics, 2017, doi:<a href=\"https://doi.org/10.1214/17-EJP42\">10.1214/17-EJP42</a>.","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “Local law for random Gram matrices,” <i>Electronic Journal of Probability</i>, vol. 22. Institute of Mathematical Statistics, 2017."},"article_processing_charge":"No","department":[{"_id":"LaEr"}],"article_number":"25","abstract":[{"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∗. ","lang":"eng"}],"publication":"Electronic Journal of Probability","publication_status":"published","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"149"}]},"author":[{"last_name":"Alt","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","first_name":"Johannes","full_name":"Alt, Johannes"},{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"first_name":"Torben H","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87"}],"doi":"10.1214/17-EJP42","_id":"1010","isi":1,"publication_identifier":{"issn":["10836489"]},"type":"journal_article","has_accepted_license":"1","volume":22,"date_updated":"2023-09-22T09:45:23Z"}