Scaling limit of multitype Galton-Watson trees with infinitely many types
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Publication:520775
DOI10.1214/15-AIHP713zbMATH Open1369.60059arXiv1405.3916OpenAlexW2962912558MaRDI QIDQ520775
Author name not available (Why is that?)
Publication date: 6 April 2017
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1405.3916
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