{"abstract":[{"text":"For large random matrices X with independent, centered entries but not necessarily identical variances, the eigenvalue density of XX* is well-approximated by a deterministic measure on ℝ. We show that the density of this measure has only square and cubic-root singularities away from zero. We also extend the bulk local law in [5] to the vicinity of these singularities.","lang":"eng"}],"volume":22,"file_date_updated":"2020-07-14T12:47:00Z","date_created":"2018-12-11T11:47:07Z","publication_status":"published","language":[{"iso":"eng"}],"publication":"Electronic Communications in Probability","scopus_import":1,"_id":"550","oa":1,"file":[{"access_level":"open_access","checksum":"0ec05303a0de190de145654237984c79","date_created":"2018-12-12T10:08:04Z","content_type":"application/pdf","date_updated":"2020-07-14T12:47:00Z","file_id":"4663","creator":"system","file_name":"IST-2018-926-v1+1_euclid.ecp.1511233247.pdf","relation":"main_file","file_size":470876}],"day":"21","publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","date_updated":"2023-09-07T12:38:08Z","publist_id":"7265","status":"public","author":[{"last_name":"Alt","first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","full_name":"Alt, Johannes"}],"article_number":"63","ddc":["539"],"type":"journal_article","has_accepted_license":"1","doi":"10.1214/17-ECP97","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"intvolume":"        22","date_published":"2017-11-21T00:00:00Z","citation":{"mla":"Alt, Johannes. “Singularities of the Density of States of Random Gram Matrices.” <i>Electronic Communications in Probability</i>, vol. 22, 63, Institute of Mathematical Statistics, 2017, doi:<a href=\"https://doi.org/10.1214/17-ECP97\">10.1214/17-ECP97</a>.","short":"J. Alt, Electronic Communications in Probability 22 (2017).","ieee":"J. Alt, “Singularities of the density of states of random Gram matrices,” <i>Electronic Communications in Probability</i>, vol. 22. Institute of Mathematical Statistics, 2017.","ama":"Alt J. Singularities of the density of states of random Gram matrices. <i>Electronic Communications in Probability</i>. 2017;22. doi:<a href=\"https://doi.org/10.1214/17-ECP97\">10.1214/17-ECP97</a>","chicago":"Alt, Johannes. “Singularities of the Density of States of Random Gram Matrices.” <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics, 2017. <a href=\"https://doi.org/10.1214/17-ECP97\">https://doi.org/10.1214/17-ECP97</a>.","apa":"Alt, J. (2017). Singularities of the density of states of random Gram matrices. <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/17-ECP97\">https://doi.org/10.1214/17-ECP97</a>","ista":"Alt J. 2017. Singularities of the density of states of random Gram matrices. Electronic Communications in Probability. 22, 63."},"title":"Singularities of the density of states of random Gram matrices","quality_controlled":"1","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"149"}]},"project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"publication_identifier":{"issn":["1083589X"]},"pubrep_id":"926","ec_funded":1,"month":"11","year":"2017"}