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The Continuum Random Tree. I

David Aldous
The Annals of Probability
Vol. 19, No. 1 (Jan., 1991), pp. 1-28
Stable URL: http://www.jstor.org/stable/2244250
Page Count: 28
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The Continuum Random Tree. I
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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 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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