TY  - JOUR
A1  - Janson, Svante
A1  - Kersting, Götz
T1  - On the total external length of the Kingman coalescent
T2  - Electronic journal of probability
N2  - 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.
KW  - coalescent
KW  - external branch
KW  - reversibility
KW  - urn model
Y1  - 2011
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/32892
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-328923
SN  - 1083-6489
N1  - This work is licensed under a Creative Commons Attribution 3.0 License  http://creativecommons.org/licenses/by/3.0/.
VL  - 16
SP  - 2203
EP  - 2218
PB  - EMIS ELibEMS
CY  - [Madralin]
ER  -