## 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)
Full Text: