{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T13:48:10Z","timestamp":1740491290214,"version":"3.38.0"},"reference-count":6,"publisher":"Cambridge University Press (CUP)","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2012,9]]},"abstract":"<jats:p>In a Galton-Watson branching process that is not extinct by the <jats:italic>n<\/jats:italic>th generation and has at least two individuals, pick two individuals at random by simple random sampling without replacement. Trace their lines of descent back in time till they meet. Call that generation <jats:italic>X<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>n<\/jats:italic>\n               <\/jats:sub> a <jats:italic>pairwise coalescence time<\/jats:italic>. Similarly, let <jats:italic>Y<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>n<\/jats:italic>\n               <\/jats:sub>\ndenote the <jats:italic>coalescence time<\/jats:italic> for the whole population of the <jats:italic>n<\/jats:italic>th generation conditioned on the event that it is not extinct. In this paper the distributions of <jats:italic>X<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>n<\/jats:italic>\n               <\/jats:sub> and <jats:italic>Y<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>n<\/jats:italic>\n               <\/jats:sub>, and their limit behaviors as <jats:italic>n<\/jats:italic> \u2192 \u221e are discussed for both the critical and subcritical cases.<\/jats:p>","DOI":"10.1017\/s0021900200009426","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T10:49:46Z","timestamp":1459248586000},"page":"627-638","source":"Crossref","is-referenced-by-count":3,"title":["Coalescence in Critical and Subcritical Galton-Watson Branching Processes"],"prefix":"10.1017","volume":"49","author":[{"given":"K. B.","family":"Athreya","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,2,4]]},"reference":[{"key":"S0021900200009426_ref3","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1032374454"},{"volume-title":"Branching Processes","year":"2004","key":"S0021900200009426_ref2"},{"volume-title":"Random Measures","year":"1986","key":"S0021900200009426_ref4"},{"key":"S0021900200009426_ref6","first-page":"602","volume":"20","year":"1975","journal-title":"Theory Prob. Appl."},{"key":"S0021900200009426_ref5","first-page":"712","volume":"120","year":"2010","journal-title":"Stoch. Process. Appl."},{"key":"S0021900200009426_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2012.06.015"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200009426","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,4,22]],"date-time":"2017-04-22T15:23:49Z","timestamp":1492874629000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200009426\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,9]]},"references-count":6,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2012,9]]}},"alternative-id":["S0021900200009426"],"URL":"https:\/\/doi.org\/10.1017\/s0021900200009426","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"type":"print","value":"0021-9002"},{"type":"electronic","value":"1475-6072"}],"subject":[],"published":{"date-parts":[[2012,9]]}}}