On the total external length of the Kingman coalescent

  • 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 Uk, 0 < k < n, of red balls after k steps exhibit an unexpected property: (U0, ... ,Un) and (Un, ... ;U0) are equal in distribution.

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Author:Svante JansonORCiDGND, Götz KerstingGND
URN:urn:nbn:de:hebis:30:3-328923
DOI:https://doi.org/10.1214/EJP.v16-955
ISSN:1083-6489
ArXiv Id:http://arxiv.org/abs/1004.5011
Parent Title (English):Electronic journal of probability
Publisher:EMIS ELibEMS
Place of publication:[Madralin]
Document Type:Article
Language:English
Date of Publication (online):2011/11/13
Date of first Publication:2011/11/13
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2014/01/29
Tag:coalescent; external branch; reversibility; urn model
Volume:16
Page Number:16
First Page:2203
Last Page:2218
Note:
This work is licensed under a Creative Commons Attribution 3.0 License  http://creativecommons.org/licenses/by/3.0/.
HeBIS-PPN:363698671
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification:60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Fxx Limit theorems [See also 28Dxx, 60B12] / 60F05 Central limit and other weak theorems
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Kxx Special processes / 60K35 Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Sammlungen:Universitätspublikationen
Licence (German):License LogoCreative Commons - Namensnennung 3.0

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