[{"date_published":"2013-05-29T00:00:00Z","page":"1-58","publication":"Electronic Journal of Probability","citation":{"short":"L. Erdös, A. Knowles, H. Yau, J. Yin, Electronic Journal of Probability 18 (2013) 1–58.","mla":"Erdös, László, et al. “The Local Semicircle Law for a General Class of Random Matrices.” Electronic Journal of Probability, vol. 18, no. 59, Institute of Mathematical Statistics, 2013, pp. 1–58, doi:10.1214/EJP.v18-2473.","chicago":"Erdös, László, Antti Knowles, Horng Yau, and Jun Yin. “The Local Semicircle Law for a General Class of Random Matrices.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2013. https://doi.org/10.1214/EJP.v18-2473.","apa":"Erdös, L., Knowles, A., Yau, H., & Yin, J. (2013). The local semicircle law for a general class of random matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/EJP.v18-2473","ieee":"L. Erdös, A. Knowles, H. Yau, and J. Yin, “The local semicircle law for a general class of random matrices,” Electronic Journal of Probability, vol. 18, no. 59. Institute of Mathematical Statistics, pp. 1–58, 2013.","ista":"Erdös L, Knowles A, Yau H, Yin J. 2013. The local semicircle law for a general class of random matrices. Electronic Journal of Probability. 18(59), 1–58."},"day":"29","has_accepted_license":"1","uri_base":"https://research-explorer.ista.ac.at","scopus_import":1,"dc":{"date":["2013"],"language":["eng"],"rights":["info:eu-repo/semantics/openAccess"],"source":["Erdös L, Knowles A, Yau H, Yin J. The local semicircle law for a general class of random matrices. Electronic Journal of Probability. 2013;18(59):1-58. doi:10.1214/EJP.v18-2473"],"title":["The local semicircle law for a general class of random matrices"],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.1214/EJP.v18-2473"],"subject":["ddc:530"],"publisher":["Institute of Mathematical Statistics"],"creator":["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/2837","https://research-explorer.ista.ac.at/download/2837/5169"],"description":["We consider a general class of N × N random matrices whose entries hij are independent up to a symmetry constraint, but not necessarily identically distributed. Our main result is a local semicircle law which improves previous results [17] both in the bulk and at the edge. The error bounds are given in terms of the basic small parameter of the model, maxi,j E|hij|2. As a consequence, we prove the universality of the local n-point correlation functions in the bulk spectrum for a class of matrices whose entries do not have comparable variances, including random band matrices with band width W ≫N1-εn with some εn > 0 and with a negligible mean-field component. In addition, we provide a coherent and pedagogical proof of the local semicircle law, streamlining and strengthening previous arguments from [17, 19, 6]."]},"file":[{"file_size":651497,"content_type":"application/pdf","creator":"system","access_level":"open_access","file_name":"IST-2016-406-v1+1_2473-13759-1-PB.pdf","checksum":"aac9e52a00cb2f5149dc9e362b5ccf44","date_updated":"2020-07-14T12:45:50Z","date_created":"2018-12-12T10:15:46Z","relation":"main_file","file_id":"5169"}],"oa_version":"Published Version","pubrep_id":"406","ddc":[],"status":"public","intvolume":" 18","_id":"2837","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng"}],"issue":"59","type":"journal_article","language":[{}],"quality_controlled":"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"},"oa":1,"month":"05","dini_type":"doc-type:article","date_created":"2018-12-11T11:59:51Z","date_updated":"2021-01-12T07:00:06Z","volume":18,"author":[{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"last_name":"Knowles","first_name":"Antti"},{"first_name":"Horng","last_name":"Yau"},{"first_name":"Jun","last_name":"Yin"}],"publication_status":"published","department":[{"_id":"LaEr","tree":[{"_id":"ResearchGroups"},{"_id":"IST"}]}],"creator":{"id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","login":"dernst"},"file_date_updated":"2020-07-14T12:45:50Z","publist_id":"3962"}]