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The Continuum Random Tree. I
Open accessAbstract
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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Metadata
- Authors
- Aldous, D.
- Venue
- The Annals of Probability
- Publisher
- Institute of Mathematical Statistics
- Published
- 1991-01-01
- Volume
- 19
- Issue
- 1
- ISSN
- 0091-1798 (ISSN-L)
- OpenAlex
- W2095181329
- Cited by
- 812
- References
- 0
- FWCI
- 11.15
- Type
- journal article
- Language
- en
- Open access
- bronze
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