{"issue":"10","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"19547"}]},"volume":406,"publication":"Communications in Mathematical Physics","has_accepted_license":"1","abstract":[{"text":"For correlated real symmetric or complex Hermitian random matrices, we prove that the local eigenvalue statistics at any cusp singularity are universal. Since the density of states typically exhibits only square root edge or cubic root cusp singularities, our result completes the proof of the Wigner–Dyson–Mehta universality conjecture in all spectral regimes for a very general class of random matrices. Previously only the bulk and the edge universality were established in this generality (Alt et al. in Ann Probab 48(2):963–1001, 2020), while cusp universality was proven only for Wigner-type matrices with independent entries (Cipolloni et al. in Pure Appl Anal 1:615–707, 2019; Erdős et al. in Commun. Math. Phys. 378:1203–1278, 2018). As our main technical input, we prove an optimal local law at the cusp using the <jats:italic>Zigzag strategy</jats:italic>, a recursive tandem of the characteristic flow method and a Green function comparison argument. Moreover, our proof of the optimal local law holds uniformly in the spectrum, thus we also provide a significantly simplified alternative proof of the local eigenvalue universality in the previously studied bulk (Erdős et al. in Forum Math. Sigma 7:E8, 2019) and edge (Alt et al. in Ann Probab 48(2):963–1001, 2020) regimes.","lang":"eng"}],"file":[{"file_size":1465827,"relation":"main_file","access_level":"open_access","date_updated":"2025-09-10T07:48:21Z","file_id":"20336","date_created":"2025-09-10T07:48:21Z","success":1,"content_type":"application/pdf","file_name":"2025_CommMathPhysics_Erdoes.pdf","creator":"dernst","checksum":"abd32af7b8ca6dc5b9080823a433986b"}],"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"intvolume":"       406","publisher":"Springer Nature","month":"09","corr_author":"1","acknowledgement":"We thank Giorgio Cipolloni for many productive discussions and the anonymous referees for several useful suggestions and spotting some typos. Open access funding provided by Institute of Science and Technology (IST Austria).","PlanS_conform":"1","OA_place":"publisher","oa_version":"Published Version","arxiv":1,"title":"Cusp universality for correlated random matrices","external_id":{"arxiv":["2410.06813"],"isi":["001565019000005"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","file_date_updated":"2025-09-10T07:48:21Z","_id":"20322","article_type":"original","isi":1,"oa":1,"OA_type":"hybrid","publication_status":"published","scopus_import":"1","doi":"10.1007/s00220-025-05417-z","department":[{"_id":"LaEr"}],"ddc":["510"],"date_updated":"2025-09-30T14:36:50Z","date_created":"2025-09-10T05:38:17Z","year":"2025","article_number":"253","quality_controlled":"1","status":"public","language":[{"iso":"eng"}],"day":"01","author":[{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László"},{"orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","last_name":"Henheik"},{"first_name":"Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","last_name":"Riabov","full_name":"Riabov, Volodymyr"}],"article_processing_charge":"Yes (via OA deal)","type":"journal_article","citation":{"ieee":"L. Erdös, S. J. Henheik, and V. Riabov, “Cusp universality for correlated random matrices,” <i>Communications in Mathematical Physics</i>, vol. 406, no. 10. Springer Nature, 2025.","chicago":"Erdös, László, Sven Joscha Henheik, and Volodymyr Riabov. “Cusp Universality for Correlated Random Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00220-025-05417-z\">https://doi.org/10.1007/s00220-025-05417-z</a>.","apa":"Erdös, L., Henheik, S. J., &#38; Riabov, V. (2025). Cusp universality for correlated random matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-025-05417-z\">https://doi.org/10.1007/s00220-025-05417-z</a>","ama":"Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. <i>Communications in Mathematical Physics</i>. 2025;406(10). doi:<a href=\"https://doi.org/10.1007/s00220-025-05417-z\">10.1007/s00220-025-05417-z</a>","mla":"Erdös, László, et al. “Cusp Universality for Correlated Random Matrices.” <i>Communications in Mathematical Physics</i>, vol. 406, no. 10, 253, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s00220-025-05417-z\">10.1007/s00220-025-05417-z</a>.","short":"L. Erdös, S.J. Henheik, V. Riabov, Communications in Mathematical Physics 406 (2025).","ista":"Erdös L, Henheik SJ, Riabov V. 2025. Cusp universality for correlated random matrices. Communications in Mathematical Physics. 406(10), 253."},"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"date_published":"2025-09-01T00:00:00Z"}