THE CONTINUUM RANDOM TREE .1.
成果类型：
Article
署名作者：
ALDOUS, D
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176990534
发表日期：
1991
页码：
1-28
关键词：
摘要：
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.
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