{"publication_status":"published","project":[{"grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"grant_number":"665385","call_identifier":"H2020","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"month":"10","oa_version":"Preprint","publication_identifier":{"eissn":["2578-5885"],"issn":["2578-5893"]},"volume":1,"year":"2019","issue":"4","language":[{"iso":"eng"}],"date_updated":"2023-09-07T12:54:12Z","date_created":"2019-03-28T10:21:17Z","publication":"Pure and Applied Analysis ","author":[{"orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","first_name":"Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","last_name":"Erdös"},{"first_name":"Torben H","full_name":"Krüger, Torben H","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","first_name":"Dominik J","full_name":"Schröder, Dominik J","last_name":"Schröder"}],"department":[{"_id":"LaEr"}],"page":"615–707","_id":"6186","status":"public","external_id":{"arxiv":["1811.04055"]},"date_published":"2019-10-12T00:00:00Z","ec_funded":1,"doi":"10.2140/paa.2019.1.615","citation":{"apa":"Cipolloni, G., Erdös, L., Krüger, T. H., &#38; Schröder, D. J. (2019). Cusp universality for random matrices, II: The real symmetric case. <i>Pure and Applied Analysis </i>. MSP. <a href=\"https://doi.org/10.2140/paa.2019.1.615\">https://doi.org/10.2140/paa.2019.1.615</a>","mla":"Cipolloni, Giorgio, et al. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” <i>Pure and Applied Analysis </i>, vol. 1, no. 4, MSP, 2019, pp. 615–707, doi:<a href=\"https://doi.org/10.2140/paa.2019.1.615\">10.2140/paa.2019.1.615</a>.","short":"G. Cipolloni, L. Erdös, T.H. Krüger, D.J. Schröder, Pure and Applied Analysis  1 (2019) 615–707.","ista":"Cipolloni G, Erdös L, Krüger TH, Schröder DJ. 2019. Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . 1(4), 615–707.","chicago":"Cipolloni, Giorgio, László Erdös, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” <i>Pure and Applied Analysis </i>. MSP, 2019. <a href=\"https://doi.org/10.2140/paa.2019.1.615\">https://doi.org/10.2140/paa.2019.1.615</a>.","ieee":"G. Cipolloni, L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices, II: The real symmetric case,” <i>Pure and Applied Analysis </i>, vol. 1, no. 4. MSP, pp. 615–707, 2019.","ama":"Cipolloni G, Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices, II: The real symmetric case. <i>Pure and Applied Analysis </i>. 2019;1(4):615–707. doi:<a href=\"https://doi.org/10.2140/paa.2019.1.615\">10.2140/paa.2019.1.615</a>"},"article_processing_charge":"No","article_type":"original","quality_controlled":"1","title":"Cusp universality for random matrices, II: The real symmetric case","oa":1,"intvolume":"         1","publisher":"MSP","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"6179"}]},"type":"journal_article","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1811.04055"}],"day":"12","abstract":[{"lang":"eng","text":"We prove that the local eigenvalue statistics of real symmetric Wigner-type\r\nmatrices near the cusp points of the eigenvalue density are universal. Together\r\nwith the companion paper [arXiv:1809.03971], which proves the same result for\r\nthe complex Hermitian symmetry class, this completes the last remaining case of\r\nthe Wigner-Dyson-Mehta universality conjecture after bulk and edge\r\nuniversalities have been established in the last years. We extend the recent\r\nDyson Brownian motion analysis at the edge [arXiv:1712.03881] to the cusp\r\nregime using the optimal local law from [arXiv:1809.03971] and the accurate\r\nlocal shape analysis of the density from [arXiv:1506.05095, arXiv:1804.07752].\r\nWe also present a PDE-based method to improve the estimate on eigenvalue\r\nrigidity via the maximum principle of the heat flow related to the Dyson\r\nBrownian motion."}]}