Invariance principles for spatial multitype Galton-Watson trees

Details Invariance principles for spatial multitype Galton-Watson trees Invariance principles for spatial multitype Galton-Watson trees

2006-10-26

arxiv.org/abs/math/0610807v1

Mathematics

Probability

44 pages

Scientific paper

We prove that critical multitype Galton-Watson trees converge after rescaling to the Brownian continuum random tree, under the hypothesis that the offspring distribution has finite covariance matrices. Our study relies on an ancestral decomposition for marked multitype trees. 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 that the resulting discrete spatial trees converge once suitably rescaled to the Brownian snake, under some suitable moment assumptions.

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