Scaling limit of multitype Galton-Watson trees with infinitely many types

Loïc de Raphelis

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arXiv · 1405.3916

Scaling limit of multitype Galton-Watson trees with infinitely many types

Loïc de Raphelis

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Abstract

We introduce a certain class of 2-type Galton-Watson trees with edge lengths. We prove that, after an adequate rescaling, the weighted height function of a forest of such trees converges in law to the reflected Brownian motion. We then use this to deduce under mild conditions an invariance principle for multitype Galton--Watson trees with a countable number of types, thus extending a result of G. Miermont on multitype Galton--Watson trees with finitely many types.

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Loïc de Raphelis. 2014-05-15. Scaling limit of multitype Galton-Watson trees with infinitely many types. https://arxiv.org/abs/1405.3916

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