{"author":[{"orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Mühlbacher, Peter","first_name":"Peter","last_name":"Mühlbacher"}],"publication":"Random matrices: Theory and applications","doi":"10.1142/s2010326319500096","publication_identifier":{"issn":["2010-3263"],"eissn":["2010-3271"]},"external_id":{"arxiv":["1802.05175"],"isi":["000477677200002"]},"citation":{"ieee":"L. Erdös and P. Mühlbacher, “Bounds on the norm of Wigner-type random matrices,” <i>Random matrices: Theory and applications</i>. World Scientific Publishing, 2018.","mla":"Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random Matrices.” <i>Random Matrices: Theory and Applications</i>, 1950009, World Scientific Publishing, 2018, doi:<a href=\"https://doi.org/10.1142/s2010326319500096\">10.1142/s2010326319500096</a>.","short":"L. Erdös, P. Mühlbacher, Random Matrices: Theory and Applications (2018).","apa":"Erdös, L., &#38; Mühlbacher, P. (2018). Bounds on the norm of Wigner-type random matrices. <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s2010326319500096\">https://doi.org/10.1142/s2010326319500096</a>","chicago":"Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random Matrices.” <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing, 2018. <a href=\"https://doi.org/10.1142/s2010326319500096\">https://doi.org/10.1142/s2010326319500096</a>.","ista":"Erdös L, Mühlbacher P. 2018. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications., 1950009.","ama":"Erdös L, Mühlbacher P. Bounds on the norm of Wigner-type random matrices. <i>Random matrices: Theory and applications</i>. 2018. doi:<a href=\"https://doi.org/10.1142/s2010326319500096\">10.1142/s2010326319500096</a>"},"ec_funded":1,"article_number":"1950009","_id":"5971","language":[{"iso":"eng"}],"year":"2018","isi":1,"project":[{"call_identifier":"FP7","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems"}],"day":"26","type":"journal_article","date_updated":"2023-09-19T14:24:05Z","month":"09","article_processing_charge":"No","publication_status":"published","date_published":"2018-09-26T00:00:00Z","abstract":[{"text":"We consider a Wigner-type ensemble, i.e. large hermitian N×N random matrices H=H∗ with centered independent entries and with a general matrix of variances Sxy=𝔼∣∣Hxy∣∣2. The norm of H is asymptotically given by the maximum of the support of the self-consistent density of states. We establish a bound on this maximum in terms of norms of powers of S that substantially improves the earlier bound 2∥S∥1/2∞ given in [O. Ajanki, L. Erdős and T. Krüger, Universality for general Wigner-type matrices, Prob. Theor. Rel. Fields169 (2017) 667–727]. The key element of the proof is an effective Markov chain approximation for the contributions of the weighted Dyck paths appearing in the iterative solution of the corresponding Dyson equation.","lang":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1802.05175"}],"department":[{"_id":"LaEr"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_created":"2019-02-13T10:40:54Z","oa_version":"Preprint","oa":1,"scopus_import":"1","publisher":"World Scientific Publishing","status":"public","title":"Bounds on the norm of Wigner-type random matrices","quality_controlled":"1"}