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January, 1991 The Continuum Random Tree. I
David Aldous
Ann. Probab. 19(1): 1-28 (January, 1991). DOI: 10.1214/aop/1176990534


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.


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David Aldous. "The Continuum Random Tree. I." Ann. Probab. 19 (1) 1 - 28, January, 1991.


Published: January, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0722.60013
MathSciNet: MR1085326
Digital Object Identifier: 10.1214/aop/1176990534

Primary: 60C05
Secondary: 05C80

Keywords: Critical branching process , Random fractal , Random tree

Rights: Copyright © 1991 Institute of Mathematical Statistics


Vol.19 • No. 1 • January, 1991
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