@article{EJP2747,
author = {Romain Abraham and Jean-François Delmas},
title = {Local limits of conditioned Galton-Watson trees: the infinite spine case},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {19},
year = {2014},
keywords = {Conditioned Galton-Watson tree, Kesten's tree},
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.},
pages = {no. 2, 1-19},
issn = {1083-6489},
doi = {10.1214/EJP.v19-2747},
url = {http://ejp.ejpecp.org/article/view/2747}}