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2011 On the Total External Length of the Kingman Coalescent
Svante Janson, Götz Kersting
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Electron. J. Probab. 16: 2203-2218 (2011). DOI: 10.1214/EJP.v16-955

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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Svante Janson. Götz Kersting. "On the Total External Length of the Kingman Coalescent." Electron. J. Probab. 16 2203 - 2218, 2011. https://doi.org/10.1214/EJP.v16-955

Information

Accepted: 13 November 2011; Published: 2011
First available in Project Euclid: 1 June 2016

zbMATH: 1245.60094
MathSciNet: MR2861672
Digital Object Identifier: 10.1214/EJP.v16-955

Subjects:
Primary: 60K35
Secondary: 60F05, 60J10

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Vol.16 • 2011
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