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The continuum random tree. I. (English) Zbl 0722.60013

Asymptotics for uniform random labelled trees on n vertices are treated from a modern stochastic process viewpoint. Three limit processes are considered. The first 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 \(\ell_ 1\). The proofs are based on a simple algorithm for generating the finite random tree and on weak convergence arguments.

MSC:

60C05 Combinatorial probability
05C80 Random graphs (graph-theoretic aspects)
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