THE CONTINUUM RANDOM TREE-III
THE CONTINUUM RANDOM TREE-III
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DOI：
10.1214/aop/1176989404
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发表时间：
1993-01-01
影响因子：
2.3
通讯作者：
ALDOUS, D
中科院分区：
文献类型：
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作者：
ALDOUS, D
设（R（k），k ≥ 1）是具有k个叶子的随机树，满足一致性条件：从R（k）中移除一个随机叶子得到R（k - 1）。然后，在一个额外的条件下，这个家庭确定一个随机连续树l，它是方便地表示为l1的随机子集。这导致了一个抽象的概念，收敛分布，作为n -->无穷大，（重标度）随机树T（n）在n个顶点的限制连续随机树l。这个概念是基于这样的假设：对于固定的k，由k个随机选择的顶点所确定的T（n）的子树收敛到R（k）.作为我们的主要例子，在后代分布的较弱条件下，总种群大小等于n的Galton-Watson分支过程的家谱可以被重标度以收敛到一个极限连续随机树，该极限连续随机树可以由布朗游程构造.
Let (R(k), k greater-than-or-equal-to 1) be random trees with k leaves, satisfying a consistency condition: Removing a random leaf from R(k) gives R(k - 1). Then under an extra condition, this family determines a random continuum tree l, which it is convenient to represent as a random subset of l1. This leads to an abstract notion of convergence in distribution, as n --> infinity, of (rescaled) random trees T(n) on n vertices to a limit continuum random tree l. The notion is based upon the assumption that, for fixed k, the subtrees of T(n) determined by k randomly chosen vertices converge to R(k).As our main example, under mild conditions on the offspring distribution, the family tree of a Galton-Watson branching process, conditioned on total population size equal to n, can be rescaled to converge to a limit continuum random tree which can be constructed from Brownian excursion.