{"_id":"10862","year":"2020","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.01597"}],"article_number":"108639","scopus_import":"1","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"publication_identifier":{"issn":["0022-1236"]},"article_type":"original","isi":1,"author":[{"full_name":"Bao, Zhigang","orcid":"0000-0003-3036-1475","last_name":"Bao","first_name":"Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László"},{"first_name":"Kevin","last_name":"Schnelli","full_name":"Schnelli, Kevin"}],"doi":"10.1016/j.jfa.2020.108639","date_updated":"2023-08-24T14:08:42Z","keyword":["Analysis"],"department":[{"_id":"LaEr"}],"citation":{"mla":"Bao, Zhigang, et al. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” <i>Journal of Functional Analysis</i>, vol. 279, no. 7, 108639, Elsevier, 2020, doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">10.1016/j.jfa.2020.108639</a>.","ista":"Bao Z, Erdös L, Schnelli K. 2020. Spectral rigidity for addition of random matrices at the regular edge. Journal of Functional Analysis. 279(7), 108639.","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” <i>Journal of Functional Analysis</i>. Elsevier, 2020. <a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">https://doi.org/10.1016/j.jfa.2020.108639</a>.","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Spectral rigidity for addition of random matrices at the regular edge,” <i>Journal of Functional Analysis</i>, vol. 279, no. 7. Elsevier, 2020.","ama":"Bao Z, Erdös L, Schnelli K. Spectral rigidity for addition of random matrices at the regular edge. <i>Journal of Functional Analysis</i>. 2020;279(7). doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">10.1016/j.jfa.2020.108639</a>","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2020). Spectral rigidity for addition of random matrices at the regular edge. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">https://doi.org/10.1016/j.jfa.2020.108639</a>","short":"Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 279 (2020)."},"acknowledgement":"Partially supported by ERC Advanced Grant RANMAT No. 338804.","quality_controlled":"1","day":"15","ec_funded":1,"oa":1,"volume":279,"publication_status":"published","type":"journal_article","date_published":"2020-10-15T00:00:00Z","publisher":"Elsevier","article_processing_charge":"No","abstract":[{"lang":"eng","text":"We consider the sum of two large Hermitian matrices A and B with a Haar unitary conjugation bringing them into a general relative position. We prove that the eigenvalue density on the scale slightly above the local eigenvalue spacing is asymptotically given by the free additive convolution of the laws of A and B as the dimension of the matrix increases. This implies optimal rigidity of the eigenvalues and optimal rate of convergence in Voiculescu's theorem. Our previous works [4], [5] established these results in the bulk spectrum, the current paper completely settles the problem at the spectral edges provided they have the typical square-root behavior. The key element of our proof is to compensate the deterioration of the stability of the subordination equations by sharp error estimates that properly account for the local density near the edge. Our results also hold if the Haar unitary matrix is replaced by the Haar orthogonal matrix."}],"intvolume":"       279","status":"public","month":"10","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"Spectral rigidity for addition of random matrices at the regular edge","issue":"7","publication":"Journal of Functional Analysis","external_id":{"isi":["000559623200009"],"arxiv":["1708.01597"]},"date_created":"2022-03-18T10:18:59Z","oa_version":"Preprint","language":[{"iso":"eng"}]}