[{"main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2103.03906"}],"title":"On the operator norm of a Hermitian random matrix with correlated entries","article_processing_charge":"No","arxiv":1,"publication":"Random Matrices: Theory and Applications","language":[{"iso":"eng"}],"article_type":"original","date_published":"2022-10-01T00:00:00Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","oa":1,"day":"01","external_id":{"isi":["000848873800001"],"arxiv":["2103.03906"]},"scopus_import":"1","issue":"4","publication_identifier":{"eissn":["2010-3271"],"issn":["2010-3263"]},"oa_version":"Preprint","doi":"10.1142/s2010326322500368","_id":"11135","year":"2022","type":"journal_article","article_number":"2250036","author":[{"id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","full_name":"Reker, Jana","last_name":"Reker","first_name":"Jana"}],"publication_status":"published","isi":1,"month":"10","date_created":"2022-04-08T07:11:12Z","intvolume":"        11","citation":{"ista":"Reker J. 2022. On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. 11(4), 2250036.","apa":"Reker, J. (2022). On the operator norm of a Hermitian random matrix with correlated entries. <i>Random Matrices: Theory and Applications</i>. World Scientific. <a href=\"https://doi.org/10.1142/s2010326322500368\">https://doi.org/10.1142/s2010326322500368</a>","mla":"Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” <i>Random Matrices: Theory and Applications</i>, vol. 11, no. 4, 2250036, World Scientific, 2022, doi:<a href=\"https://doi.org/10.1142/s2010326322500368\">10.1142/s2010326322500368</a>.","ama":"Reker J. On the operator norm of a Hermitian random matrix with correlated entries. <i>Random Matrices: Theory and Applications</i>. 2022;11(4). doi:<a href=\"https://doi.org/10.1142/s2010326322500368\">10.1142/s2010326322500368</a>","short":"J. Reker, Random Matrices: Theory and Applications 11 (2022).","ieee":"J. Reker, “On the operator norm of a Hermitian random matrix with correlated entries,” <i>Random Matrices: Theory and Applications</i>, vol. 11, no. 4. World Scientific, 2022.","chicago":"Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” <i>Random Matrices: Theory and Applications</i>. World Scientific, 2022. <a href=\"https://doi.org/10.1142/s2010326322500368\">https://doi.org/10.1142/s2010326322500368</a>."},"volume":11,"quality_controlled":"1","date_updated":"2023-08-03T06:32:22Z","abstract":[{"text":"We consider a correlated NxN Hermitian random matrix with a polynomially decaying metric correlation structure. By calculating the trace of the moments of the matrix and using the summable decay of the cumulants, we show that its operator norm is stochastically dominated by one.","lang":"eng"}],"keyword":["Discrete Mathematics and Combinatorics","Statistics","Probability and Uncertainty","Statistics and Probability","Algebra and Number Theory"],"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"publisher":"World Scientific"},{"day":"26","oa":1,"doi":"10.1142/s2010326319500096","oa_version":"Preprint","scopus_import":"1","external_id":{"arxiv":["1802.05175"],"isi":["000477677200002"]},"publication_identifier":{"issn":["2010-3263"],"eissn":["2010-3271"]},"arxiv":1,"title":"Bounds on the norm of Wigner-type random matrices","article_processing_charge":"No","language":[{"iso":"eng"}],"publication":"Random matrices: Theory and applications","main_file_link":[{"url":"https://arxiv.org/abs/1802.05175","open_access":"1"}],"status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_published":"2018-09-26T00:00:00Z","quality_controlled":"1","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"}],"date_updated":"2023-09-19T14:24:05Z","citation":{"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.","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>.","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>","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>."},"publisher":"World Scientific Publishing","department":[{"_id":"LaEr"}],"_id":"5971","year":"2018","article_number":"1950009","type":"journal_article","date_created":"2019-02-13T10:40:54Z","author":[{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"first_name":"Peter","last_name":"Mühlbacher","full_name":"Mühlbacher, Peter"}],"ec_funded":1,"month":"09","isi":1,"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804"}],"publication_status":"published"}]