On the total external length of the Kingman coalescent
2011 (English)In: Electronic Journal of Probability, ISSN 1083-6489, Vol. 16, 2203-2218 p.Article in journal (Refereed) Published
In this paper we prove asymptotic normality of the total length of external branches in Kingman's coalescent. The proof uses an embedded Markov chain, which can be described as follows: Take an urn with n black balls. Empty it in n steps according to the rule: In each step remove a randomly chosen pair of balls and replace it by one red ball. Finally remove the last remaining ball. Then the numbers U(k), 0 <= k <= n, of red balls after k steps exhibit an unexpected property: (U(0), ... , U(n)) and (U(n), ... , U(0)) are equal in distribution.
Place, publisher, year, edition, pages
2011. Vol. 16, 2203-2218 p.
coalescent, external branch, reversibility, urn model
IdentifiersURN: urn:nbn:se:uu:diva-166070ISI: 000297757200002OAI: oai:DiVA.org:uu-166070DiVA: diva2:476904