{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T06:05:28Z","timestamp":1787724328175,"version":"build-2784847793"},"reference-count":26,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2014,7,10]],"date-time":"2014-07-10T00:00:00Z","timestamp":1404950400000},"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":[[2014,11]]},"abstract":"<jats:p>For 1 &lt; \u03b1 &lt; 2 we derive the asymptotic distribution of the total length of<jats:italic>external<\/jats:italic>branches of a Beta(2 \u2212 \u03b1, \u03b1)-coalescent as the number<jats:italic>n<\/jats:italic>of leaves becomes large. It turns out that the fluctuations of the external branch length follow those of \u03c4<jats:italic><jats:sub>n<\/jats:sub><\/jats:italic><jats:sup>2\u2212\u03b1<\/jats:sup>over the entire parameter regime, where \u03c4<jats:italic><jats:sub>n<\/jats:sub><\/jats:italic>denotes the random number of coalescences that bring the<jats:italic>n<\/jats:italic>lineages down to one. This is in contrast to the fluctuation behaviour of the total branch length, which exhibits a transition at<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0963548314000297_inline1\"\/><jats:tex-math>$\\alpha_0 = (1+\\sqrt 5)\/2$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>([18]).<\/jats:p>","DOI":"10.1017\/s0963548314000297","type":"journal-article","created":{"date-parts":[[2014,7,10]],"date-time":"2014-07-10T07:41:23Z","timestamp":1404978083000},"page":"1010-1027","source":"Crossref","is-referenced-by-count":17,"title":["The Total External Branch Length of Beta-Coalescents"],"prefix":"10.1017","volume":"23","author":[{"given":"IULIA","family":"DAHMER","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"G\u00d6TZ","family":"KERSTING","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"ANTON","family":"WAKOLBINGER","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,7,10]]},"reference":[{"key":"S0963548314000297_ref8","doi-asserted-by":"crossref","unstructured":"Boom E. 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