Scaling limits of Markov branching trees and Galton-Watson trees conditioned on the number of vertices with out-degree in a given set

Details Scaling limits of Markov branching trees and Galton-Watson trees conditioned on the number of vertices with out-degree in a given set Scaling limits of Markov branching trees and Galton-Watson trees conditioned on the number of vertices with out-degree in a given set

2011-05-12

arxiv.org/abs/1105.2528v1

Mathematics

Probability

23 pages

Scientific paper

We generalize recent results of Haas and Miermont to obtain scaling limits of Markov branching trees whose size is specified by the number of nodes whose out-degree lies in a given set. We then show that this implies that the scaling limit of finite variance Galton-Watson trees condition on the number of nodes whose out-degree lies in a given set is the Brownian continuum random tree. The key to this is a generalization of the classical Otter-Dwass formula.

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