{"article_type":"original","publisher":"Institute of Mathematical Statistics","isi":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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.","language":[{"iso":"eng"}],"scopus_import":"1","date_created":"2023-01-16T10:04:38Z","page":"1-38","_id":"12290","intvolume":"        27","date_published":"2022-09-12T00:00:00Z","publication_identifier":{"eissn":["1083-6489"]},"type":"journal_article","corr_author":"1","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"title":"Optimal multi-resolvent local laws for Wigner matrices","author":[{"last_name":"Cipolloni","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","full_name":"Erdös, László"},{"last_name":"Schröder","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","full_name":"Schröder, Dominik J"}],"department":[{"_id":"LaEr"}],"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"quality_controlled":"1","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"}],"external_id":{"isi":["000910863700003"]},"year":"2022","citation":{"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.","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>","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>","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>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 27 (2022) 1–38.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 27, 1–38.","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>."},"has_accepted_license":"1","publication":"Electronic Journal of Probability","month":"09","ec_funded":1,"date_updated":"2025-04-14T07:57:19Z","doi":"10.1214/22-ejp838","publication_status":"published","status":"public","ddc":["510"],"oa_version":"Published Version","oa":1,"file_date_updated":"2023-01-30T11:59:21Z","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"file":[{"checksum":"bb647b48fbdb59361210e425c220cdcb","access_level":"open_access","relation":"main_file","date_created":"2023-01-30T11:59:21Z","file_name":"2022_ElecJournProbability_Cipolloni.pdf","file_id":"12464","success":1,"content_type":"application/pdf","creator":"dernst","file_size":502149,"date_updated":"2023-01-30T11:59:21Z"}],"day":"12","article_processing_charge":"No","volume":27}