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

Douglas Rizzolo

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arXiv · 1105.2528

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

Douglas Rizzolo

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Abstract

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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Douglas Rizzolo. 2011-05-12. Scaling limits of Markov branching trees and Galton-Watson trees conditioned on the number of vertices with out-degree in a given set. https://arxiv.org/abs/1105.2528

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