Local limits of conditioned Galton-Watson trees II: the condensation case
Probability
2014-07-01 v1
Abstract
We provide a complete picture of the local convergence of critical or subcritical Galton-Watson tree conditioned on having a large number of individuals with out-degree in a given set. The generic case, where the limit is a random tree with an infinite spine has been treated in a previous paper. We focus here on the non-generic case, where the limit is a random tree with a node with infinite out-degree. This case corresponds to the so-called condensation phenomenon.
Keywords
Cite
@article{arxiv.1311.6683,
title = {Local limits of conditioned Galton-Watson trees II: the condensation case},
author = {Romain Abraham and Jean-Francois Delmas},
journal= {arXiv preprint arXiv:1311.6683},
year = {2014}
}