On the Total External Length of the Kingman Coalescent

Svante Janson (Uppsala University)
Götz Kersting (Goethe university Frankfurt)

Abstract


We prove asymptotic normality of the total length of external branches in the Kingman coalescent. The proof uses an embedded Markov chain, which can be described as follows: Take an urn with black balls. Empty it step by step 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 of red balls form a Markov chain with an unexpected property: It is time-reversible.

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Pages: 2203-2218

Publication Date: November 13, 2011

DOI: 10.1214/EJP.v16-955

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