Invariance principles for spatial multitype Galton–Watson trees
Grégory Miermont (2008)
Annales de l'I.H.P. Probabilités et statistiques
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We prove that critical multitype Galton–Watson trees converge after rescaling to the brownian continuum random tree, under the hypothesis that the offspring distribution is irreducible and has finite covariance matrices. Our study relies on an ancestral decomposition for marked multitype trees, and an induction on the number of types. We then couple the genealogical structure with a spatial motion, whose step distribution may depend on the structure of the tree in a local way, and show...