The Annals of Probability
- Ann. Probab.
- Volume 19, Number 1 (1991), 1-28.
The Continuum Random Tree. I
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 $l_1$. 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.
Ann. Probab., Volume 19, Number 1 (1991), 1-28.
First available in Project Euclid: 19 April 2007
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Aldous, David. The Continuum Random Tree. I. Ann. Probab. 19 (1991), no. 1, 1--28. doi:10.1214/aop/1176990534. https://projecteuclid.org/euclid.aop/1176990534