--- res: bibo_abstract: - "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.@eng" bibo_authorlist: - foaf_Person: foaf_givenName: Giorgio foaf_name: Cipolloni, Giorgio foaf_surname: Cipolloni foaf_workInfoHomepage: http://www.librecat.org/personId=42198EFA-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-4901-7992 - foaf_Person: foaf_givenName: László foaf_name: Erdös, László foaf_surname: Erdös foaf_workInfoHomepage: http://www.librecat.org/personId=4DBD5372-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0001-5366-9603 - foaf_Person: foaf_givenName: Torben H foaf_name: Krüger, Torben H foaf_surname: Krüger foaf_workInfoHomepage: http://www.librecat.org/personId=3020C786-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-4821-3297 - foaf_Person: foaf_givenName: Dominik J foaf_name: Schröder, Dominik J foaf_surname: Schröder foaf_workInfoHomepage: http://www.librecat.org/personId=408ED176-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-2904-1856 bibo_doi: 10.2140/paa.2019.1.615 bibo_issue: '4' bibo_volume: 1 dct_date: 2019^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/2578-5893 - http://id.crossref.org/issn/2578-5885 dct_language: eng dct_publisher: MSP@ dct_title: 'Cusp universality for random matrices, II: The real symmetric case@' ...