{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:58:03Z","timestamp":1760029083226},"reference-count":23,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2017,8,1]],"date-time":"2017-08-01T00:00:00Z","timestamp":1501545600000},"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":[[2018,3]]},"abstract":"<jats:p>In this paper we prove lower and upper bounds for the extinction time of the contact process on random geometric graphs with connection radius tending to infinity. We obtain that for any infection rate \u03bb &gt; 0, the contact process on these graphs survives a time super-exponential in the number of vertices.<\/jats:p>","DOI":"10.1017\/s0963548317000372","type":"journal-article","created":{"date-parts":[[2017,8,1]],"date-time":"2017-08-01T02:14:27Z","timestamp":1501553667000},"page":"162-185","source":"Crossref","is-referenced-by-count":6,"title":["Super-Exponential Extinction Time of the Contact Process on Random Geometric Graphs"],"prefix":"10.1017","volume":"27","author":[{"given":"VAN HAO","family":"CAN","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2017,8,1]]},"reference":[{"key":"S0963548317000372_ref5","doi-asserted-by":"publisher","DOI":"10.1214\/09-AOP471"},{"key":"S0963548317000372_ref1","unstructured":"Berger N. , Borgs C. , Chayes J. T. and Saberi A. (2005) On the spread of viruses on the internet. In SODA '05: Proc. 16th Annual ACM\u2013SIAM Symposium on Discrete Algorithms, SIAM, pp. 301\u2013310."},{"key":"S0963548317000372_ref15","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1214\/aop\/1024404279","article-title":"Domination by product measure","volume":"25","author":"Liggett","year":"1997","journal-title":"Ann. Probab."},{"key":"S0963548317000372_ref3","unstructured":"Can V. H. (2016) Processus de contact sur des graphes al\u00e9atoires. PhD thesis, University of Aix\u2013Marseille."},{"key":"S0963548317000372_ref4","doi-asserted-by":"publisher","DOI":"10.1214\/EJP.v20-3859"},{"key":"S0963548317000372_ref21","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198506263.001.0001"},{"key":"S0963548317000372_ref20","doi-asserted-by":"publisher","DOI":"10.24033\/asens.2307"},{"key":"S0963548317000372_ref23","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(90)90206-W"},{"key":"S0963548317000372_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/BF00959619"},{"key":"S0963548317000372_ref16","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1993-031-3"},{"key":"S0963548317000372_ref6","first-page":"385","article-title":"The contact process on finite homogeneous trees revisited","volume":"11","author":"Cranston","year":"2014","journal-title":"ALEA: Lat. Am. J. Probab. Math. Statist."},{"key":"S0963548317000372_ref2","doi-asserted-by":"publisher","DOI":"10.24166\/im.08.2017"},{"key":"S0963548317000372_ref7","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176993140"},{"key":"S0963548317000372_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-012-9710-y"},{"key":"S0963548317000372_ref18","doi-asserted-by":"publisher","DOI":"10.1214\/EJP.v18-2512"},{"key":"S0963548317000372_ref19","doi-asserted-by":"publisher","DOI":"10.1214\/16-EJP4476"},{"key":"S0963548317000372_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03990-8"},{"key":"S0963548317000372_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2016.01.001"},{"key":"S0963548317000372_ref22","doi-asserted-by":"crossref","unstructured":"Preciado V. M. and Jadbabaie A. (2009) Spectral analysis of virus spreading in random geometric networks. In Proc. IEEE Conference on Decision and Control, IEEE, pp. 4802\u20134807.","DOI":"10.1109\/CDC.2009.5400615"},{"key":"S0963548317000372_ref10","doi-asserted-by":"publisher","DOI":"10.1239\/aap\/1427814586"},{"key":"S0963548317000372_ref12","first-page":"69","article-title":"Long paths and cycles in a random lattice","volume":"33","author":"Grimmett","year":"1985","journal-title":"Ann. Discrete Math."},{"key":"S0963548317000372_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03981-6"},{"key":"S0963548317000372_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1784-8_33"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548317000372","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,14]],"date-time":"2019-04-14T18:56:17Z","timestamp":1555268177000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548317000372\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,1]]},"references-count":23,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,3]]}},"alternative-id":["S0963548317000372"],"URL":"https:\/\/doi.org\/10.1017\/s0963548317000372","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,8,1]]}}}