The Annals of Probability

The Continuum Random Tree. I

David Aldous

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Abstract

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.

Article information

Source
Ann. Probab. Volume 19, Number 1 (1991), 1-28.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990534

Digital Object Identifier
doi:10.1214/aop/1176990534

Mathematical Reviews number (MathSciNet)
MR1085326

Zentralblatt MATH identifier
0722.60013

JSTOR
links.jstor.org

Subjects
Primary: 60C05: Combinatorial probability
Secondary: 05C80: Random graphs [See also 60B20]

Keywords
Random tree random fractal critical branching process

Citation

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


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