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On the Total External Length of the Kingman Coalescent


 
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1. Title Title of document On the Total External Length of the Kingman Coalescent
 
2. Creator Author's name, affiliation, country Svante Janson; Uppsala University; Sweden
 
2. Creator Author's name, affiliation, country Götz Kersting; Goethe university Frankfurt; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) coalescent, external branch, reversibility, urn model
 
3. Subject Subject classification 60K35; 60F05; 60J10
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2011-11-13
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/955
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-955
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 16
 
12. Language English=en
 
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