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The external lengths in Kingman's coalescent - MaRDI portal

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The external lengths in Kingman's coalescent

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Publication:6502843

arXiv1004.5011MaRDI QIDQ6502843

Author name not available (Why is that?)


Abstract: 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 descriped 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 leq k leq n, of red balls after k steps exhibits an unexpected property: (U_0,...,U_n) and (U_n,..., U_0) are equal in distribution.





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