Scaling limit of multitype Galton-Watson trees with infinitely many types
Probability
2015-11-03 v3
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.
Keywords
Cite
@article{arxiv.1405.3916,
title = {Scaling limit of multitype Galton-Watson trees with infinitely many types},
author = {Loïc de Raphelis},
journal= {arXiv preprint arXiv:1405.3916},
year = {2015}
}