[{"external_id":{"isi":["000416389200001"]},"language":[{"iso":"eng"}],"file":[{"date_created":"2018-12-12T10:08:04Z","relation":"main_file","creator":"system","file_size":470876,"checksum":"0ec05303a0de190de145654237984c79","date_updated":"2020-07-14T12:47:00Z","file_name":"IST-2018-926-v1+1_euclid.ecp.1511233247.pdf","content_type":"application/pdf","access_level":"open_access","file_id":"4663"}],"fulldoi":"https://doi.org/10.1214/17-ECP97","isi":1,"publist_id":"7265","date_published":"2017-11-21T00:00:00Z","day":"21","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"date_updated":"2026-04-08T14:11:36Z","title":"Singularities of the density of states of random Gram matrices","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"}],"file_date_updated":"2020-07-14T12:47:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publisher":"Institute of Mathematical Statistics","doi":"10.1214/17-ECP97","_id":"550","status":"public","type":"journal_article","project":[{"grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"author":[{"last_name":"Alt","full_name":"Alt, Johannes","first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"}],"publication_status":"published","ddc":["539"],"pubrep_id":"926","year":"2017","oa":1,"article_processing_charge":"No","month":"11","oa_version":"Published Version","intvolume":"        22","citation":{"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.","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>","short":"J. Alt, Electronic Communications in Probability 22 (2017).","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>.","ista":"Alt J. 2017. Singularities of the density of states of random Gram matrices. Electronic Communications in Probability. 22, 63.","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>.","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>"},"corr_author":"1","has_accepted_license":"1","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"149"}]},"date_created":"2018-12-11T11:47:07Z","scopus_import":"1","department":[{"_id":"LaEr"}],"publication":"Electronic Communications in Probability","article_number":"63","ec_funded":1,"volume":22,"publication_identifier":{"issn":["1083-589X"]},"quality_controlled":"1"}]