On the total external length of the Kingman coalescent
On the total external length of the Kingman coalescent
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DOI：
10.1214/ejp.v16-955
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发表时间：
2011-11-13
影响因子：
1.4
通讯作者：
Kersting, Goetz
中科院分区：
文献类型：
--
作者：
Janson, Svante;Kersting, Goetz
本文证明了金曼聚结中外支总长度的渐近正态性。该证明使用嵌入马尔可夫链，其描述如下：取一个有n个黑球的瓮。根据规则，在n步中清空它：在每一步中移除随机选择的一对球，并用一个红球替换它。最后取出最后一个剩下的球。然后是数字U-k 0
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 U-k, 0