{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,27]],"date-time":"2024-08-27T11:09:56Z","timestamp":1724756996282},"reference-count":25,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2017,8,7]],"date-time":"2017-08-07T00:00:00Z","timestamp":1502064000000},"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":[[2017,11]]},"abstract":"We consider the complete graph\ud835\udf05n<\/jats:sub><\/jats:italic>onn<\/jats:italic>vertices with exponential meann<\/jats:italic>edge lengths. WritingCij<\/jats:sub><\/jats:italic>for the weight of the smallest-weight path between verticesi, j<\/jats:italic>\u2208 [n<\/jats:italic>], Janson [18] showed that maxi,j<\/jats:italic>\u2208[n<\/jats:italic>]<\/jats:sub>C<\/jats:italic>ij<\/jats:italic>\/logn<\/jats:italic><\/jats:sub>converges in probability to 3. We extend these results by showing that maxi,j<\/jats:italic>\u2208[n<\/jats:italic>]<\/jats:sub>Cij<\/jats:sub><\/jats:italic>\u2212 3 logn<\/jats:italic>converges in distribution to some limiting random variable that can be identified via a maximization procedure on a limiting infinite random structure. Interestingly, this limiting random variable has also appeared as the weak limit of the re-centredgraph diameter<\/jats:italic>of the barely supercritical Erd\u0151s\u2013R\u00e9nyi random graph in [22].<\/jats:p>","DOI":"10.1017\/s0963548317000232","type":"journal-article","created":{"date-parts":[[2017,8,7]],"date-time":"2017-08-07T02:19:28Z","timestamp":1502072368000},"page":"797-825","source":"Crossref","is-referenced-by-count":4,"title":["Diameter of the Stochastic Mean-Field Model of Distance"],"prefix":"10.1017","volume":"26","author":[{"given":"SHANKAR","family":"BHAMIDI","sequence":"first","affiliation":[]},{"given":"REMCO","family":"VAN DER HOFSTAD","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2017,8,7]]},"reference":[{"key":"S0963548317000232_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(85)90058-7"},{"key":"S0963548317000232_ref7","doi-asserted-by":"publisher","DOI":"10.1214\/14-AAP1034"},{"key":"S0963548317000232_ref22","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548310000325"},{"key":"S0963548317000232_ref8","doi-asserted-by":"publisher","DOI":"10.1137\/120899534"},{"key":"S0963548317000232_ref4","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139107174.004"},{"key":"S0963548317000232_ref18","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548399003892"},{"key":"S0963548317000232_ref6","first-page":"1","volume-title":"Probability on Discrete Structures","author":"Aldous","year":"2004"},{"key":"S0963548317000232_ref14","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20342"},{"key":"S0963548317000232_ref24","first-page":"1","article-title":"A survey of recursive trees","volume":"51","author":"Smythe","year":"1994","journal-title":"Teor. \u012cmov\u012br. 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