Random labelled trees and their branching networks
Random labelled trees and their branching networks
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DOI：
10.1017/s1446788700016517
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发表时间：
1980-12
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影响因子：
--
通讯作者：
G. Grimmett
中科院分区：
文献类型：
--
作者：
G. Grimmett
N个顶点上的随机根标号树具有与分枝型过程渐近相同的形状，其中Poisson族大小为参数1的分枝过程的每一代都被一个附加成员随机地添加到该代中的一个族中。在这篇注记中，我们使用这个概率表示来推导出从根到除其自身之外最近的内皮层的距离的渐近分布。
Abstract A random rooted labelled tree on n vertices has asymptotically the same shape as a branching-type process, in which each generation of a branching process with Poisson family sizes, parameter one, is supplemented by a single additional member added at random to one of the families in that generation. In this note we use this probabilistic representation to deduce the asymptotic distribution of the distance from the root to the nearest endertex other than itself.