{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T02:06:48Z","timestamp":1775527608976,"version":"3.50.1"},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T00:00:00Z","timestamp":1755561600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2026,3]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Asymptotic properties of random graph sequences, like the occurrence of a giant component or full connectivity in Erd\u00f6s\u2013R\u00e9nyi graphs, are usually derived with very specific choices for the defining parameters. The question arises as to what extent those parameter choices may be perturbed without losing the asymptotic property. For two sequences of graph distributions, asymptotic equivalence (convergence in total variation) and contiguity have been considered by Janson (2010) and others; here we use so-called remote contiguity to show that connectivity properties are preserved in more heavily perturbed Erd\u00f6s\u2013R\u00e9nyi graphs. The techniques we demonstrate here with random graphs also extend to general asymptotic properties, e.g. in more complex large-graph limits, scaling limits, large-sample limits, etc.<\/jats:p>","DOI":"10.1017\/jpr.2025.10029","type":"journal-article","created":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T10:30:20Z","timestamp":1755599420000},"page":"316-333","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Contiguity and remote contiguity of some random graphs"],"prefix":"10.1017","volume":"63","author":[{"given":"Bas J. K.","family":"Kleijn","sequence":"first","affiliation":[{"name":"University of Amsterdam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1207-3437","authenticated-orcid":false,"given":"Stefano","family":"Rizzelli","sequence":"additional","affiliation":[{"name":"University of Padova"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2025,8,19]]},"reference":[{"key":"S0021900225100296_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548300001735"},{"key":"S0021900225100296_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4946-7"},{"key":"S0021900225100296_ref6","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20297"},{"key":"S0021900225100296_ref7","doi-asserted-by":"publisher","DOI":"10.1214\/20-AOS1952"},{"key":"S0021900225100296_ref4","author":"Greenwood","year":"1985"},{"key":"S0021900225100296_ref13","doi-asserted-by":"publisher","DOI":"10.1017\/9781316779422"},{"key":"S0021900225100296_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/jpr.2019.100"},{"key":"S0021900225100296_ref11","doi-asserted-by":"publisher","DOI":"10.1214\/21-AOS2160"},{"key":"S0021900225100296_ref12","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804373"},{"key":"S0021900225100296_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1166-2"},{"key":"S0021900225100296_ref1","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20168"},{"key":"S0021900225100296_ref8","volume-title":"Locally Asymptotically Normal Families of Distributions: Certain Approximations to Families of Distributions and Their Use in the Theory of Estimation and Testing Hypotheses","author":"Le Cam","year":"1960"},{"key":"S0021900225100296_ref2","doi-asserted-by":"publisher","DOI":"10.5486\/PMD.1959.6.3-4.12"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900225100296","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T01:25:59Z","timestamp":1775525159000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900225100296\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,19]]},"references-count":13,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,3]]}},"alternative-id":["S0021900225100296"],"URL":"https:\/\/doi.org\/10.1017\/jpr.2025.10029","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,19]]},"assertion":[{"value":"\u00a9 The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}