{"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","month":"09","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"oa_version":"Preprint","publication_identifier":{"issn":["2010-3263"],"eissn":["2010-3271"]},"title":"Bounds on the norm of Wigner-type random matrices","article_processing_charge":"No","isi":1,"date_published":"2018-09-26T00:00:00Z","main_file_link":[{"url":"https://arxiv.org/abs/1802.05175","open_access":"1"}],"type":"journal_article","department":[{"_id":"LaEr"}],"_id":"5971","doi":"10.1142/s2010326319500096","author":[{"last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Peter","full_name":"Mühlbacher, Peter","last_name":"Mühlbacher"}],"scopus_import":"1","publisher":"World Scientific Publishing","language":[{"iso":"eng"}],"date_updated":"2023-09-19T14:24:05Z","article_number":"1950009","abstract":[{"lang":"eng","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."}],"quality_controlled":"1","oa":1,"ec_funded":1,"publication_status":"published","year":"2018","day":"26","citation":{"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>.","ista":"Erdös L, Mühlbacher P. 2018. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications., 1950009.","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.","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>","short":"L. Erdös, P. Mühlbacher, Random Matrices: Theory and Applications (2018).","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>","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>."},"status":"public","date_created":"2019-02-13T10:40:54Z","publication":"Random matrices: Theory and applications","external_id":{"arxiv":["1802.05175"],"isi":["000477677200002"]}}