{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,16]],"date-time":"2024-06-16T15:10:49Z","timestamp":1718550649955},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2017,5,29]],"date-time":"2017-05-29T00:00:00Z","timestamp":1496016000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2017,9]]},"abstract":"We identify the asymptotic probability of a configuration model CMn<\/jats:italic><\/jats:sub>(d<\/jats:italic>) producing a connected<\/jats:italic> graph within its critical window for connectivity that is identified by the number of vertices of degree 1 and 2, as well as the expected degree. In this window, the probability that the graph is connected converges to a non-trivial value, and the size of the complement of the giant component weakly converges to a finite random variable. Under a finite second moment condition we also derive the asymptotics of the connectivity probability conditioned on simplicity, from which follows the asymptotic number of simple connected graphs with a prescribed degree sequence.<\/jats:p>","DOI":"10.1017\/s0963548317000177","type":"journal-article","created":{"date-parts":[[2017,5,29]],"date-time":"2017-05-29T02:33:44Z","timestamp":1496025224000},"page":"660-680","source":"Crossref","is-referenced-by-count":12,"title":["Critical Window for Connectivity in the Configuration Model"],"prefix":"10.1017","volume":"26","author":[{"given":"LORENZO","family":"FEDERICO","sequence":"first","affiliation":[]},{"given":"REMCO","family":"VAN DER HOFSTAD","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2017,5,29]]},"reference":[{"key":"S0963548317000177_ref7","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20231"},{"key":"S0963548317000177_ref2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511814068"},{"key":"S0963548317000177_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/S0095-8956(81)80021-4"},{"key":"S0963548317000177_ref8","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032718"},{"key":"S0963548317000177_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02458840"},{"key":"S0963548317000177_ref11","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548398003526"},{"key":"S0963548317000177_ref6","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1417528471"},{"key":"S0963548317000177_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/9781316779422"},{"key":"S0963548317000177_ref4","doi-asserted-by":"publisher","DOI":"10.1214\/07-AAP490"},{"key":"S0963548317000177_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548308009644"},{"key":"S0963548317000177_ref9","first-page":"165","volume-title":"Random Graphs (Pozna\u0144 1989)","author":"\u0141uczak","year":"1992"},{"key":"S0963548317000177_ref10","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.3240060204"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548317000177","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,16]],"date-time":"2019-04-16T23:58:20Z","timestamp":1555459100000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548317000177\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,29]]},"references-count":12,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2017,9]]}},"alternative-id":["S0963548317000177"],"URL":"https:\/\/doi.org\/10.1017\/s0963548317000177","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,5,29]]}}}