Scaling limits of Markov branching trees and Galton-Watson trees conditioned on the number of vertices with out-degree in a given set
By Douglas Rizzolo. 2011
49 citations recorded by the source corpus.
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.
Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/2259c6ce90df88a92a06fcf8148cb9ea1cf0ec2c
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In Condensed Matter Physics
In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- Invariance principles for Galton-Watson trees conditioned on the number of leaves (2011, background): “The main result of [31] considers a random tree distributed according to Pμ[ · | ζA(τ) = n], where it is assumed that 0 ∈ A.”
- Local limits of conditioned Galton-Watson trees: the infinite spine case (2013, methodology): “Such conditioning has already been studied by Rizzolo [24], see also Mimami [20], but for global scaling limits and not local limits.”