THE CONTINUUM RANDOM TREE .1.
THE CONTINUUM RANDOM TREE .1.
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DOI：
10.1214/aop/1176990534
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发表时间：
1991-01-01
影响因子：
2.3
通讯作者：
ALDOUS, D
中科院分区：
文献类型：
--
作者：
ALDOUS, D
关于n阶均匀随机标号树的精确和渐近结果已被组合学家广泛研究。 在这里，我们从现代随机过程的观点来对待渐近性。 有三个极限过程。 一个是无限离散树。 另外两个最自然地表示为无限维空间l1的连续二维分形树状子集。 一个是紧凑型;另一个是无界的和自相似的。证明是基于一个简单的算法，用于产生有限的随机树和弱收敛的论点。 这些极限过程的分布性质将在后面讨论。
Exact and asymptotic results for the uniform random labelled tree on n vertices have been studied extensively by combinatorialists. Here we treat asymptotics from a modern stochastic process viewpoint. There are three limit processes. One is an infinite discrete tree. The other two are most naturally represented as continuous two-dimensional fractal tree-like subsets of the infinite-dimensional space l1. One is compact; the other is unbounded and self-similar.The proofs are based upon a simple algorithm for generating the finite random tree and upon weak convergence arguments. Distributional properties of these limit processes will be discussed in a sequel.