{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,11,11]],"date-time":"2024-11-11T13:10:34Z","timestamp":1731330634387,"version":"3.28.0"},"reference-count":29,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2024,10,3]],"date-time":"2024-10-03T00:00:00Z","timestamp":1727913600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100010661","name":"Horizon 2020 Framework Programme","doi-asserted-by":"publisher","award":["945045"],"id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003246","name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","award":["024.002.003"],"id":[{"id":"10.13039\/501100003246","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[2025,1]]},"abstract":"Abstract<\/jats:title>Let be an arbitrary field and be a sequence of sparse weighted Erd\u0151s\u2013R\u00e9nyi random graphs on vertices with edge probability , where weights from are assigned to the edges according to a matrix . We show that the normalized rank of the adjacency matrix of converges to a constant, and derive the limiting expression. Our result shows that for the general class of sparse symmetric matrices under consideration, the asymptotics of the normalized rank are independent of the edge weights and even the field, in the sense that the limiting constant for the general case coincides with the one previously established for adjacency matrices of sparse nonweighted Erd\u0151s\u2013R\u00e9nyi matrices over . Our proof, which is purely combinatorial in its nature, is based on an intricate extension of a novel perturbation approach to the symmetric setting.<\/jats:p>","DOI":"10.1002\/rsa.21258","type":"journal-article","created":{"date-parts":[[2024,10,3]],"date-time":"2024-10-03T08:56:26Z","timestamp":1727945786000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The rank of sparse symmetric matrices over arbitrary fields"],"prefix":"10.1002","volume":"66","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-1331-9697","authenticated-orcid":false,"given":"Remco","family":"van der Hofstad","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science Eindhoven University of Technology Eindhoven The Netherlands"}]},{"ORCID":"http:\/\/orcid.org\/0009-0004-8182-311X","authenticated-orcid":false,"given":"Noela","family":"M\u00fcller","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science Eindhoven University of Technology Eindhoven The Netherlands"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-6823-9331","authenticated-orcid":false,"given":"Haodong","family":"Zhu","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science Eindhoven University of Technology Eindhoven The Netherlands"}]}],"member":"311","published-online":{"date-parts":[[2024,10,3]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548314000285"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.68.214403"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1098-2418(199803)12:2<111::AID-RSA1>3.0.CO;2-#"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-019-3897-3"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00440-021-01038-4"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.86.2621"},{"issue":"3","key":"e_1_2_9_8_1","doi-asserted-by":"crossref","DOI":"10.1214\/18-AOP1293","article-title":"Largest eigenvalues of sparse inhomogeneous Erd\u0151s\u2013R\u00e9nyi graphs","volume":"47","author":"Benaych\u2010Georges F.","year":"2019","journal-title":"Ann. 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