{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T02:10:35Z","timestamp":1649038235943},"reference-count":29,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2020,5,18]],"date-time":"2020-05-18T00:00:00Z","timestamp":1589760000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2020,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We study random unlabelled <jats:italic>k<\/jats:italic>-trees by combining the colouring approach by Gainer-Dewar and Gessel (2014) with the cycle-pointing method by Bodirsky, Fusy, Kang and Vigerske (2011). Our main applications are Gromov\u2013Hausdorff\u2013Prokhorov and Benjamini\u2013Schramm limits that describe their asymptotic geometric shape on a global and local scale as the number of (<jats:italic>k<\/jats:italic> + 1)-cliques tends to infinity.<\/jats:p>","DOI":"10.1017\/s0963548320000164","type":"journal-article","created":{"date-parts":[[2020,5,18]],"date-time":"2020-05-18T08:23:10Z","timestamp":1589790190000},"page":"722-746","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Graph limits of random unlabelled <i>k<\/i>-trees"],"prefix":"10.1017","volume":"29","author":[{"given":"Emma Yu","family":"Jin","sequence":"first","affiliation":[]},{"given":"Benedikt","family":"Stufler","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2020,5,18]]},"reference":[{"key":"S0963548320000164_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511662980.003"},{"key":"S0963548320000164_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-10217-2_19"},{"key":"S0963548320000164_ref20","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(69)80119-5"},{"key":"S0963548320000164_ref16","volume-title":"Graphical Enumeration","author":"Harary","year":"1973"},{"key":"S0963548320000164_ref17","unstructured":"[17] Iriza, A. D. (2015) Enumeration and random generation of unlabeled classes of graphs: A practical study of cycle-pointing and the dissymmetry theorem. Master\u2019s thesis, Princeton University."},{"key":"S0963548320000164_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(81)90052-9"},{"key":"S0963548320000164_ref3","doi-asserted-by":"publisher","DOI":"10.37236\/1089"},{"key":"S0963548320000164_ref26","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20771"},{"key":"S0963548320000164_ref19","doi-asserted-by":"publisher","DOI":"10.24033\/asens.2108"},{"key":"S0963548320000164_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-015-0039-1"},{"key":"S0963548320000164_ref23","unstructured":"[23] Stufler, B. (2016) Limits of random tree-like discrete structures. arXiv:1612.02580"},{"key":"S0963548320000164_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2014.05.002"},{"key":"S0963548320000164_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(69)80120-1"},{"key":"S0963548320000164_ref4","volume-title":"Vol. 67 of Encyclopedia of Mathematics and its Applications","author":"Bergeron","year":"1998"},{"key":"S0963548320000164_ref8","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20802"},{"key":"S0963548320000164_ref5","doi-asserted-by":"publisher","DOI":"10.1137\/100790082"},{"key":"S0963548320000164_ref9","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176995896"},{"key":"S0963548320000164_ref10","volume-title":"Analytic Combinatorics","author":"Flajolet","year":"2010"},{"key":"S0963548320000164_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(71)90023-9"},{"key":"S0963548320000164_ref12","doi-asserted-by":"publisher","DOI":"10.1006\/aama.2001.0771"},{"key":"S0963548320000164_ref13","doi-asserted-by":"publisher","DOI":"10.37236\/2615"},{"key":"S0963548320000164_ref24","unstructured":"[24] Stufler, B. (2017) Asymptotic properties of random unlabelled block-weighted graphs. arXiv:1712.01301"},{"key":"S0963548320000164_ref21","doi-asserted-by":"publisher","DOI":"10.2307\/1969046"},{"key":"S0963548320000164_ref22","doi-asserted-by":"publisher","DOI":"10.1007\/BF02546665"},{"key":"S0963548320000164_ref25","doi-asserted-by":"publisher","DOI":"10.1214\/16-AIHP741"},{"key":"S0963548320000164_ref27","doi-asserted-by":"publisher","DOI":"10.37236\/7328"},{"key":"S0963548320000164_ref28","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20833"},{"key":"S0963548320000164_ref29","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548319000336"},{"key":"S0963548320000164_ref15","doi-asserted-by":"publisher","DOI":"10.1112\/S002557930000245X"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548320000164","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,14]],"date-time":"2020-09-14T12:06:23Z","timestamp":1600085183000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548320000164\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,18]]},"references-count":29,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["S0963548320000164"],"URL":"https:\/\/doi.org\/10.1017\/s0963548320000164","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5,18]]},"assertion":[{"value":"\u00a9 The Author(s), 2020. Published by Cambridge University Press","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 (http:\/\/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"}]}}