{"oa_version":"Published Version","issue":"3-4","quality_controlled":"1","scopus_import":"1","title":"Universality for general Wigner-type matrices","language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","file_size":988843,"access_level":"open_access","relation":"main_file","file_name":"IST-2017-657-v1+2_s00440-016-0740-2.pdf","date_created":"2018-12-12T10:08:25Z","checksum":"29f5a72c3f91e408aeb9e78344973803","creator":"system","file_id":"4686","date_updated":"2020-07-14T12:44:44Z"}],"intvolume":"       169","pubrep_id":"657","publist_id":"5930","date_published":"2017-12-01T00:00:00Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"01","year":"2017","publisher":"Springer","ec_funded":1,"abstract":[{"lang":"eng","text":"We consider the local eigenvalue distribution of large self-adjoint N×N random matrices H=H∗ with centered independent entries. In contrast to previous works the matrix of variances sij=\\mathbbmE|hij|2 is not assumed to be stochastic. Hence the density of states is not the Wigner semicircle law. Its possible shapes are described in the companion paper (Ajanki et al. in Quadratic Vector Equations on the Complex Upper Half Plane. arXiv:1506.05095). We show that as N grows, the resolvent, G(z)=(H−z)−1, converges to a diagonal matrix, diag(m(z)), where m(z)=(m1(z),…,mN(z)) solves the vector equation −1/mi(z)=z+∑jsijmj(z) that has been analyzed in Ajanki et al. (Quadratic Vector Equations on the Complex Upper Half Plane. arXiv:1506.05095). We prove a local law down to the smallest spectral resolution scale, and bulk universality for both real symmetric and complex hermitian symmetry classes."}],"publication_status":"published","publication":"Probability Theory and Related Fields","_id":"1337","doi":"10.1007/s00440-016-0740-2","author":[{"first_name":"Oskari H","full_name":"Ajanki, Oskari H","last_name":"Ajanki","id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"orcid":"0000-0002-4821-3297","first_name":"Torben H","full_name":"Krüger, Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","last_name":"Krüger"}],"publication_identifier":{"issn":["01788051"]},"isi":1,"has_accepted_license":"1","type":"journal_article","date_updated":"2023-09-20T11:14:17Z","volume":169,"oa":1,"file_date_updated":"2020-07-14T12:44:44Z","ddc":["510","530"],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","external_id":{"isi":["000414358400002"]},"project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"status":"public","page":"667 - 727","month":"12","date_created":"2018-12-11T11:51:27Z","citation":{"ieee":"O. H. Ajanki, L. Erdös, and T. H. Krüger, “Universality for general Wigner-type matrices,” <i>Probability Theory and Related Fields</i>, vol. 169, no. 3–4. Springer, pp. 667–727, 2017.","short":"O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields 169 (2017) 667–727.","ama":"Ajanki OH, Erdös L, Krüger TH. Universality for general Wigner-type matrices. <i>Probability Theory and Related Fields</i>. 2017;169(3-4):667-727. doi:<a href=\"https://doi.org/10.1007/s00440-016-0740-2\">10.1007/s00440-016-0740-2</a>","mla":"Ajanki, Oskari H., et al. “Universality for General Wigner-Type Matrices.” <i>Probability Theory and Related Fields</i>, vol. 169, no. 3–4, Springer, 2017, pp. 667–727, doi:<a href=\"https://doi.org/10.1007/s00440-016-0740-2\">10.1007/s00440-016-0740-2</a>.","apa":"Ajanki, O. H., Erdös, L., &#38; Krüger, T. H. (2017). Universality for general Wigner-type matrices. <i>Probability Theory and Related Fields</i>. Springer. <a href=\"https://doi.org/10.1007/s00440-016-0740-2\">https://doi.org/10.1007/s00440-016-0740-2</a>","ista":"Ajanki OH, Erdös L, Krüger TH. 2017. Universality for general Wigner-type matrices. Probability Theory and Related Fields. 169(3–4), 667–727.","chicago":"Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Universality for General Wigner-Type Matrices.” <i>Probability Theory and Related Fields</i>. Springer, 2017. <a href=\"https://doi.org/10.1007/s00440-016-0740-2\">https://doi.org/10.1007/s00440-016-0740-2</a>."},"department":[{"_id":"LaEr"}],"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).  ","article_processing_charge":"Yes (via OA deal)"}