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We calculate rigorously the first expansion terms for the Gilbert disk model, the hyper-cubic model, the Gaussian connection kernel, and a coordinate-wise Cauchy kernel.<\/jats:p>","DOI":"10.1017\/s0963548324000270","type":"journal-article","created":{"date-parts":[[2024,11,8]],"date-time":"2024-11-08T05:34:06Z","timestamp":1731044046000},"page":"158-209","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Expansion of the critical intensity for the random connection model"],"prefix":"10.1017","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8629-4796","authenticated-orcid":false,"given":"Matthew","family":"Dickson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3749-7431","authenticated-orcid":false,"given":"Markus","family":"Heydenreich","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2024,11,8]]},"reference":[{"key":"S0963548324000270_ref8","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548321000365"},{"key":"S0963548324000270_ref5","unstructured":"[HHLM22] Heydenreich, M. , van der Hofstad, R. , Last, G. and Matzke, K. (2022) Lace expansion and mean-field behavior for the random connection model. Ann. Inst. H. Poincar\u00e9 Probab. Statist. arXiv preprint: 1908.11356"},{"key":"S0963548324000270_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548300001607"},{"key":"S0963548324000270_ref14","doi-asserted-by":"publisher","DOI":"10.3923\/ajms.2011.66.70"},{"key":"S0963548324000270_ref3","doi-asserted-by":"publisher","DOI":"10.1137\/0109045"},{"key":"S0963548324000270_ref10","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20074"},{"key":"S0963548324000270_ref13","doi-asserted-by":"publisher","DOI":"10.1063\/1.443316"},{"key":"S0963548324000270_ref11","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1008956687"},{"key":"S0963548324000270_ref2","unstructured":"[DH22] Dickson, M. and Heydenreich, M. 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