Local limits of conditioned Galton-Watson trees I: the infinite spine case
Probability
2014-07-01 v4
Abstract
We give a necessary and sufficient condition for the convergence in distribution of a conditioned Galton-Watson tree to Kesten's tree. This yields elementary proofs of Kesten's result as well as other known results on local limit of conditioned Galton-Watson trees. We then apply this condition to get new results, in the critical and sub-critical cases, on the limit in distribution of a Galton-Watson tree conditioned on having a large number of individuals with out-degree in a given set.
Keywords
Cite
@article{arxiv.1304.4035,
title = {Local limits of conditioned Galton-Watson trees I: the infinite spine case},
author = {Romain Abraham and Jean-Francois Delmas},
journal= {arXiv preprint arXiv:1304.4035},
year = {2014}
}