[{"ec_funded":1,"publist_id":"4739","file_date_updated":"2020-07-14T12:45:34Z","creator":{"login":"apreinsp","id":"4435EBFC-F248-11E8-B48F-1D18A9856A87"},"article_number":"33","author":[{"first_name":"Alex","last_name":"Bloemendal"},{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Antti","last_name":"Knowles"},{"first_name":"Horng","last_name":"Yau"},{"first_name":"Jun","last_name":"Yin"}],"volume":19,"date_updated":"2021-01-12T06:56:07Z","dini_type":"doc-type:article","date_created":"2018-12-11T11:56:25Z","department":[{"tree":[{"_id":"ResearchGroups"},{"_id":"IST"}],"_id":"LaEr"}],"publication_status":"published","publication_identifier":{"issn":[]},"month":"03","message":"CC BY 3.0","language":[{}],"oa":1,"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","short":"CC BY (4.0)","image":"/images/cc_by.png"},"project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","abstract":[{"lang":"eng"}],"type":"journal_article","pubrep_id":"427","file":[{"access_level":"open_access","file_name":"IST-2016-427-v1+1_3054-16624-4-PB.pdf","file_size":810150,"content_type":"application/pdf","creator":"system","relation":"main_file","file_id":"5055","checksum":"7eb297ff367a2ee73b21b6dd1e1948e4","date_updated":"2020-07-14T12:45:34Z","date_created":"2018-12-12T10:14:06Z"}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2225","intvolume":" 19","status":"public","ddc":[],"has_accepted_license":"1","uri_base":"https://research-explorer.ista.ac.at","day":"15","dc":{"creator":["Bloemendal, Alex","Erdös, László","Knowles, Antti","Yau, Horng","Yin, Jun"],"type":["info:eu-repo/semantics/article","doc-type:article","text","http://purl.org/coar/resource_type/c_6501"],"identifier":["https://research-explorer.ista.ac.at/record/2225","https://research-explorer.ista.ac.at/download/2225/5055"],"description":["We consider sample covariance matrices of the form X∗X, where X is an M×N matrix with independent random entries. We prove the isotropic local Marchenko-Pastur law, i.e. we prove that the resolvent (X∗X−z)−1 converges to a multiple of the identity in the sense of quadratic forms. More precisely, we establish sharp high-probability bounds on the quantity ⟨v,(X∗X−z)−1w⟩−⟨v,w⟩m(z), where m is the Stieltjes transform of the Marchenko-Pastur law and v,w∈CN. We require the logarithms of the dimensions M and N to be comparable. Our result holds down to scales Iz≥N−1+ε and throughout the entire spectrum away from 0. We also prove analogous results for generalized Wigner matrices.\r\n"],"date":["2014"],"language":["eng"],"rights":["info:eu-repo/semantics/openAccess"],"source":["Bloemendal A, Erdös L, Knowles A, Yau H, Yin J. Isotropic local laws for sample covariance and generalized Wigner matrices. Electronic Journal of Probability. 2014;19. doi:10.1214/EJP.v19-3054"],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.1214/EJP.v19-3054","info:eu-repo/semantics/altIdentifier/issn/10836489","info:eu-repo/grantAgreement/EC/FP7/338804"],"publisher":["Institute of Mathematical Statistics"],"subject":["ddc:510"],"title":["Isotropic local laws for sample covariance and generalized Wigner matrices"]},"date_published":"2014-03-15T00:00:00Z","citation":{"apa":"Bloemendal, A., Erdös, L., Knowles, A., Yau, H., & Yin, J. (2014). Isotropic local laws for sample covariance and generalized Wigner matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/EJP.v19-3054","ieee":"A. Bloemendal, L. Erdös, A. Knowles, H. Yau, and J. Yin, “Isotropic local laws for sample covariance and generalized Wigner matrices,” Electronic Journal of Probability, vol. 19. Institute of Mathematical Statistics, 2014.","ista":"Bloemendal A, Erdös L, Knowles A, Yau H, Yin J. 2014. Isotropic local laws for sample covariance and generalized Wigner matrices. Electronic Journal of Probability. 19, 33.","short":"A. Bloemendal, L. Erdös, A. Knowles, H. Yau, J. Yin, Electronic Journal of Probability 19 (2014).","mla":"Bloemendal, Alex, et al. “Isotropic Local Laws for Sample Covariance and Generalized Wigner Matrices.” Electronic Journal of Probability, vol. 19, 33, Institute of Mathematical Statistics, 2014, doi:10.1214/EJP.v19-3054.","chicago":"Bloemendal, Alex, László Erdös, Antti Knowles, Horng Yau, and Jun Yin. “Isotropic Local Laws for Sample Covariance and Generalized Wigner Matrices.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2014. https://doi.org/10.1214/EJP.v19-3054."},"publication":"Electronic Journal of Probability"}]