{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T07:06:54Z","timestamp":1779174414546,"version":"3.51.4"},"reference-count":15,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T00:00:00Z","timestamp":1772582400000},"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":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2026,5]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We identify the size of the largest connected component in a subcritical inhomogeneous random graph with a kernel of preferential attachment type. The component is polynomial in the graph size with an explicitly given exponent, which is strictly larger than the exponent for the largest degree in the graph. This is in stark contrast to the behaviour of inhomogeneous random graphs with a kernel of rank one. Our proof uses local approximation by branching random walks going well beyond the weak local limit and novel results on subcritical killed branching random walks.<\/jats:p>","DOI":"10.1017\/s096354832610039x","type":"journal-article","created":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T04:46:02Z","timestamp":1772599562000},"page":"414-432","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["The largest subcritical component in inhomogeneous random graphs of preferential attachment type"],"prefix":"10.1017","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8917-3789","authenticated-orcid":false,"given":"Peter","family":"M\u00f6rters","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00rcxh774","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Cologne"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-1512-1815","authenticated-orcid":false,"given":"Nick","family":"Schleicher","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00rcxh774","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Cologne"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2026,3,4]]},"reference":[{"key":"S096354832610039X_ref5","doi-asserted-by":"publisher","DOI":"10.1214\/11-AOP697"},{"key":"S096354832610039X_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2019.07.017"},{"key":"S096354832610039X_ref7","doi-asserted-by":"publisher","DOI":"10.1214\/07-AAP490"},{"key":"S096354832610039X_ref2","doi-asserted-by":"publisher","DOI":"10.2307\/3213258"},{"key":"S096354832610039X_ref14","unstructured":"[14] Ray, R. (2024) Stochastic Processes on Preferential Attachment Models: Understanding Global Structures from Local Properties (PhD Thesis). Eindhoven University of Technology, Mathematics and Computer Science."},{"key":"S096354832610039X_ref1","doi-asserted-by":"publisher","DOI":"10.1214\/13-AOP842"},{"key":"S096354832610039X_ref12","first-page":"14:1","volume-title":"AofA 2024, Volume 302 of LIPIcs","author":"M\u00f6rters","year":"2024"},{"key":"S096354832610039X_ref11","unstructured":"[11] M\u00f6rters, P. (2022) Lecture notes on random graphs. Available at https:\/\/www.mi.uni-koeln.de\/~moerters\/lectures\/RandomGraphs.pdf."},{"key":"S096354832610039X_ref15","volume-title":"Branching Random Walks: \u00c9cole d\u2019\u00c9t\u00e9 de Probabilit\u00e9s de Saint-Flour XLII \u2013 2012. Lecture Notes in Mathematics","author":"Shi","year":"2016"},{"key":"S096354832610039X_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/BF00534830"},{"key":"S096354832610039X_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s004400050256"},{"key":"S096354832610039X_ref9","volume-title":"Lectures on the Poisson Process, Volume 7 of IMS Textbook","author":"Last","year":"2018"},{"key":"S096354832610039X_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1862-3_17"},{"key":"S096354832610039X_ref4","unstructured":"[4] Banerjee, S. , Bhamidi, S. , van der Hofstad, R. and Ray, R. (2025) Non-equilibrium coagulation processes and subcritical percolation on evolving networks. ArXiv preprint, 2512.15561."},{"key":"S096354832610039X_ref3","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20168"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S096354832610039X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T06:13:10Z","timestamp":1779171190000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S096354832610039X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,4]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,5]]}},"alternative-id":["S096354832610039X"],"URL":"https:\/\/doi.org\/10.1017\/s096354832610039x","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,4]]},"assertion":[{"value":"\u00a9 The Author(s), 2026. 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 (https:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution and reproduction, provided the original article 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"}]}}