The Continuum Random Tree. I
Aldous, David
Ann. Probab., Tome 19 (1991) no. 4, p. 1-28 / Harvested from Project Euclid
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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.
Publié le : 1991-01-14
Classification:  Random tree,  random fractal,  critical branching process,  60C05,  05C80 
@article{1176990534,
     author = {Aldous, David},
     title = {The Continuum Random Tree. I},
     journal = {Ann. Probab.},
     volume = {19},
     number = {4},
     year = {1991},
     pages = { 1-28},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176990534}
}

Aldous, David. The Continuum Random Tree. I. Ann. Probab., Tome 19 (1991) no. 4, pp.  1-28. http://gdmltest.u-ga.fr/item/1176990534/