{"arxiv":1,"date_published":"2025-12-01T00:00:00Z","author":[{"full_name":"Riabov, Volodymyr","first_name":"Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","last_name":"Riabov"}],"oa":1,"publication_status":"published","title":"Linear Eigenvalue statistics at the cusp","OA_place":"publisher","PlanS_conform":"1","article_processing_charge":"Yes (via OA deal)","corr_author":"1","OA_type":"hybrid","citation":{"apa":"Riabov, V. (2025). Linear Eigenvalue statistics at the cusp. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-025-01373-w\">https://doi.org/10.1007/s00440-025-01373-w</a>","chicago":"Riabov, Volodymyr. “Linear Eigenvalue Statistics at the Cusp.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00440-025-01373-w\">https://doi.org/10.1007/s00440-025-01373-w</a>.","short":"V. Riabov, Probability Theory and Related Fields 193 (2025) 1183–1237.","mla":"Riabov, Volodymyr. “Linear Eigenvalue Statistics at the Cusp.” <i>Probability Theory and Related Fields</i>, vol. 193, Springer Nature, 2025, pp. 1183–237, doi:<a href=\"https://doi.org/10.1007/s00440-025-01373-w\">10.1007/s00440-025-01373-w</a>.","ieee":"V. Riabov, “Linear Eigenvalue statistics at the cusp,” <i>Probability Theory and Related Fields</i>, vol. 193. Springer Nature, pp. 1183–1237, 2025.","ista":"Riabov V. 2025. Linear Eigenvalue statistics at the cusp. Probability Theory and Related Fields. 193, 1183–1237.","ama":"Riabov V. Linear Eigenvalue statistics at the cusp. <i>Probability Theory and Related Fields</i>. 2025;193:1183-1237. doi:<a href=\"https://doi.org/10.1007/s00440-025-01373-w\">10.1007/s00440-025-01373-w</a>"},"file_date_updated":"2025-12-30T13:10:05Z","isi":1,"abstract":[{"lang":"eng","text":"We establish universal Gaussian fluctuations for the mesoscopic linear eigenvalue statistics in the vicinity of the cusp-like singularities of the limiting spectral density for Wigner-type random matrices. Prior to this work, the linear eigenvalue statistics at the cusp-like singularities were not studied in any ensemble. Our analysis covers not only the exact cusps but the entire transitionary regime from the square-root singularity at a regular edge through the sharp cusp to the bulk. We identify a new one-parameter family of functionals that govern the limiting bias and variance, continuously interpolating between the previously known formulas in the bulk and at a regular edge. Since cusps are the only possible singularities besides the regular edges, our result gives a complete description of the linear eigenvalue statistics in all regimes."}],"publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2025","intvolume":"       193","department":[{"_id":"LaEr"}],"publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"month":"12","day":"01","oa_version":"Published Version","scopus_import":"1","status":"public","_id":"19598","has_accepted_license":"1","article_type":"original","ddc":["510"],"quality_controlled":"1","publication":"Probability Theory and Related Fields","language":[{"iso":"eng"}],"file":[{"success":1,"checksum":"700229b280725c0d6aad0d71362cce5f","access_level":"open_access","date_updated":"2025-12-30T13:10:05Z","creator":"dernst","content_type":"application/pdf","date_created":"2025-12-30T13:10:05Z","file_id":"20916","relation":"main_file","file_name":"2025_ProbTheoryRelatFields_Riabov.pdf","file_size":919213}],"date_created":"2025-04-20T22:01:28Z","date_updated":"2025-12-30T13:10:23Z","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"20575"}]},"doi":"10.1007/s00440-025-01373-w","acknowledgement":"I would like to express my gratitude to László Erdős for his careful guidance and supervision of my work. I am also thankful to Jana Reker and Joscha Henheik for many helpful discussions. Open access funding provided by Institute of Science and Technology (IST Austria).","license":"https://creativecommons.org/licenses/by/4.0/","external_id":{"arxiv":["2307.07432"],"isi":["001466997300001"]},"type":"journal_article","tmp":{"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","short":"CC BY (4.0)"},"page":"1183-1237","volume":193}