{"quality_controlled":"1","day":"29","abstract":[{"text":"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 &gt; 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].","lang":"eng"}],"status":"public","date_updated":"2021-01-12T07:00:06Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"intvolume":"        18","pubrep_id":"406","volume":18,"has_accepted_license":"1","date_published":"2013-05-29T00:00:00Z","ddc":["530"],"year":"2013","file":[{"relation":"main_file","content_type":"application/pdf","date_updated":"2020-07-14T12:45:50Z","file_size":651497,"file_name":"IST-2016-406-v1+1_2473-13759-1-PB.pdf","date_created":"2018-12-12T10:15:46Z","checksum":"aac9e52a00cb2f5149dc9e362b5ccf44","creator":"system","file_id":"5169","access_level":"open_access"}],"date_created":"2018-12-11T11:59:51Z","publication":"Electronic Journal of Probability","department":[{"_id":"LaEr"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"1-58","publist_id":"3962","author":[{"first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"full_name":"Knowles, Antti","first_name":"Antti","last_name":"Knowles"},{"full_name":"Yau, Horng","first_name":"Horng","last_name":"Yau"},{"last_name":"Yin","full_name":"Yin, Jun","first_name":"Jun"}],"language":[{"iso":"eng"}],"file_date_updated":"2020-07-14T12:45:50Z","publication_status":"published","oa":1,"scopus_import":1,"publisher":"Institute of Mathematical Statistics","citation":{"apa":"Erdös, L., Knowles, A., Yau, H., &#38; Yin, J. (2013). The local semicircle law for a general class of random matrices. <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/EJP.v18-2473\">https://doi.org/10.1214/EJP.v18-2473</a>","short":"L. Erdös, A. Knowles, H. Yau, J. Yin, Electronic Journal of Probability 18 (2013) 1–58.","ieee":"L. Erdös, A. Knowles, H. Yau, and J. Yin, “The local semicircle law for a general class of random matrices,” <i>Electronic Journal of Probability</i>, vol. 18, no. 59. Institute of Mathematical Statistics, pp. 1–58, 2013.","mla":"Erdös, László, et al. “The Local Semicircle Law for a General Class of Random Matrices.” <i>Electronic Journal of Probability</i>, vol. 18, no. 59, Institute of Mathematical Statistics, 2013, pp. 1–58, doi:<a href=\"https://doi.org/10.1214/EJP.v18-2473\">10.1214/EJP.v18-2473</a>.","chicago":"Erdös, László, Antti Knowles, Horng Yau, and Jun Yin. “The Local Semicircle Law for a General Class of Random Matrices.” <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics, 2013. <a href=\"https://doi.org/10.1214/EJP.v18-2473\">https://doi.org/10.1214/EJP.v18-2473</a>.","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.","ama":"Erdös L, Knowles A, Yau H, Yin J. The local semicircle law for a general class of random matrices. <i>Electronic Journal of Probability</i>. 2013;18(59):1-58. doi:<a href=\"https://doi.org/10.1214/EJP.v18-2473\">10.1214/EJP.v18-2473</a>"},"type":"journal_article","oa_version":"Published Version","title":"The local semicircle law for a general class of random matrices","month":"05","issue":"59","doi":"10.1214/EJP.v18-2473","_id":"2837"}