{"date_published":"2022-09-12T00:00:00Z","day":"12","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"quality_controlled":"1","oa":1,"month":"09","date_updated":"2025-04-14T07:57:19Z","intvolume":"        27","acknowledgement":"L. Erdős was supported by ERC Advanced Grant “RMTBeyond” No. 101020331. D. Schröder was supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","abstract":[{"text":"We prove local laws, i.e. optimal concentration estimates for arbitrary products of resolvents of a Wigner random matrix with deterministic matrices in between. We find that the size of such products heavily depends on whether some of the deterministic matrices are traceless. Our estimates correctly account for this dependence and they hold optimally down to the smallest possible spectral scale.","lang":"eng"}],"file_date_updated":"2023-01-30T11:59:21Z","type":"journal_article","isi":1,"article_type":"original","page":"1-38","corr_author":"1","author":[{"last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"date_created":"2023-01-16T10:04:38Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"12290","status":"public","article_processing_charge":"No","department":[{"_id":"LaEr"}],"ec_funded":1,"doi":"10.1214/22-ejp838","ddc":["510"],"has_accepted_license":"1","publication_status":"published","license":"https://creativecommons.org/licenses/by/4.0/","title":"Optimal multi-resolvent local laws for Wigner matrices","external_id":{"isi":["000910863700003"]},"publication_identifier":{"eissn":["1083-6489"]},"publication":"Electronic Journal of Probability","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"year":"2022","publisher":"Institute of Mathematical Statistics","language":[{"iso":"eng"}],"volume":27,"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"fulldoi":"https://doi.org/10.1214/22-ejp838","file":[{"creator":"dernst","relation":"main_file","file_id":"12464","content_type":"application/pdf","date_updated":"2023-01-30T11:59:21Z","file_name":"2022_ElecJournProbability_Cipolloni.pdf","checksum":"bb647b48fbdb59361210e425c220cdcb","file_size":502149,"date_created":"2023-01-30T11:59:21Z","success":1,"access_level":"open_access"}],"oa_version":"Published Version","scopus_import":"1","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 27 (2022) 1–38.","mla":"Cipolloni, Giorgio, et al. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” <i>Electronic Journal of Probability</i>, vol. 27, Institute of Mathematical Statistics, 2022, pp. 1–38, doi:<a href=\"https://doi.org/10.1214/22-ejp838\">10.1214/22-ejp838</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Optimal multi-resolvent local laws for Wigner matrices. <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-ejp838\">https://doi.org/10.1214/22-ejp838</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics, 2022. <a href=\"https://doi.org/10.1214/22-ejp838\">https://doi.org/10.1214/22-ejp838</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Optimal multi-resolvent local laws for Wigner matrices. <i>Electronic Journal of Probability</i>. 2022;27:1-38. doi:<a href=\"https://doi.org/10.1214/22-ejp838\">10.1214/22-ejp838</a>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 27, 1–38.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal multi-resolvent local laws for Wigner matrices,” <i>Electronic Journal of Probability</i>, vol. 27. Institute of Mathematical Statistics, pp. 1–38, 2022."}}