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On the total external length of the Kingman coalescent
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2011 (English)In: Electronic Journal of Probability, ISSN 1083-6489, Vol. 16, 2203-2218 p.Article in journal (Refereed) Published
Abstract [en]

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.
Keyword [en]
coalescent, external branch, reversibility, urn model
National Category
URN: urn:nbn:se:uu:diva-166070ISI: 000297757200002OAI: oai:DiVA.org:uu-166070DiVA: diva2:476904
Available from: 2012-01-12 Created: 2012-01-10 Last updated: 2012-02-16Bibliographically approved

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