[{"oa_version":"Preprint","status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"5971","abstract":[{"lang":"eng"}],"type":"journal_article","date_published":"2018-09-26T00:00:00Z","publication":"Random matrices: Theory and applications","citation":{"mla":"Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random Matrices.” Random Matrices: Theory and Applications, 1950009, World Scientific Publishing, 2018, doi:10.1142/s2010326319500096.","short":"L. Erdös, P. Mühlbacher, Random Matrices: Theory and Applications (2018).","chicago":"Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random Matrices.” Random Matrices: Theory and Applications. World Scientific Publishing, 2018. https://doi.org/10.1142/s2010326319500096.","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,” Random matrices: Theory and applications. World Scientific Publishing, 2018.","apa":"Erdös, L., & Mühlbacher, P. (2018). Bounds on the norm of Wigner-type random matrices. Random Matrices: Theory and Applications. World Scientific Publishing. https://doi.org/10.1142/s2010326319500096"},"day":"26","uri_base":"https://research-explorer.ista.ac.at","article_processing_charge":"No","scopus_import":"1","dc":{"language":["eng"],"date":["2018"],"publisher":["World Scientific Publishing"],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.1142/s2010326319500096","info:eu-repo/semantics/altIdentifier/issn/2010-3263","info:eu-repo/semantics/altIdentifier/issn/2010-3271","info:eu-repo/semantics/altIdentifier/wos/000477677200002","info:eu-repo/semantics/altIdentifier/arxiv/1802.05175","info:eu-repo/grantAgreement/EC/FP7/338804"],"title":["Bounds on the norm of Wigner-type random matrices"],"rights":["info:eu-repo/semantics/openAccess"],"source":["Erdös L, Mühlbacher P. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications. 2018. doi:10.1142/s2010326319500096"],"creator":["Erdös, László","Mühlbacher, Peter"],"description":["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."],"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/5971"]},"dini_type":"doc-type:article","date_created":"2019-02-13T10:40:54Z","date_updated":"2023-09-19T14:24:05Z","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"},{"last_name":"Mühlbacher","first_name":"Peter"}],"publication_status":"published","department":[{"tree":[{"_id":"ResearchGroups"},{"_id":"IST"}],"_id":"LaEr"}],"creator":{"login":"dernst","id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},"ec_funded":1,"article_number":"1950009","language":[{}],"quality_controlled":"1","isi":1,"project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"external_id":{"arxiv":[],"isi":[]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1802.05175"}],"oa":1,"month":"09","publication_identifier":{"issn":[],"eissn":[]}}]