{"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","file":[{"creator":"dernst","checksum":"b75fdad606ab507dc61109e0907d86c0","date_updated":"2022-07-29T07:22:08Z","file_size":652573,"date_created":"2022-07-29T07:22:08Z","content_type":"application/pdf","relation":"main_file","file_name":"2022_JourFunctionalAnalysis_Cipolloni.pdf","file_id":"11690","success":1,"access_level":"open_access"}],"article_number":"109394","article_type":"original","publisher":"Elsevier","department":[{"_id":"LaEr"}],"oa":1,"abstract":[{"lang":"eng","text":"We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to eitW for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices."}],"oa_version":"Published Version","date_published":"2022-04-15T00:00:00Z","file_date_updated":"2022-07-29T07:22:08Z","publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"date_created":"2022-02-06T23:01:30Z","language":[{"iso":"eng"}],"article_processing_charge":"Yes (via OA deal)","title":"Thermalisation for Wigner matrices","issue":"8","day":"15","intvolume":"       282","isi":1,"license":"https://creativecommons.org/licenses/by/4.0/","publication_status":"published","volume":282,"ddc":["500"],"scopus_import":"1","month":"04","publication":"Journal of Functional Analysis","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Journal of Functional Analysis 282 (2022).","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Thermalisation for Wigner matrices,” <i>Journal of Functional Analysis</i>, vol. 282, no. 8. Elsevier, 2022.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Thermalisation for Wigner Matrices.” <i>Journal of Functional Analysis</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.jfa.2022.109394\">https://doi.org/10.1016/j.jfa.2022.109394</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Thermalisation for Wigner matrices. <i>Journal of Functional Analysis</i>. 2022;282(8). doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109394\">10.1016/j.jfa.2022.109394</a>","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Thermalisation for Wigner matrices. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2022.109394\">https://doi.org/10.1016/j.jfa.2022.109394</a>","mla":"Cipolloni, Giorgio, et al. “Thermalisation for Wigner Matrices.” <i>Journal of Functional Analysis</i>, vol. 282, no. 8, 109394, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109394\">10.1016/j.jfa.2022.109394</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Thermalisation for Wigner matrices. Journal of Functional Analysis. 282(8), 109394."},"status":"public","acknowledgement":"We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to  for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices.","external_id":{"isi":["000781239100004"],"arxiv":["2102.09975"]},"author":[{"first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"last_name":"Erdös","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László"},{"first_name":"Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"date_updated":"2023-08-02T14:12:35Z","has_accepted_license":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","year":"2022","_id":"10732","doi":"10.1016/j.jfa.2022.109394","quality_controlled":"1"}