Abstract
Abstract
We study the local convergence of critical Galton–Watson trees under various conditionings. We give a sufficient condition, which serves to cover all previous known results, for the convergence in distribution of a conditioned Galton–Watson tree to Kesten’s tree. We also propose a new proof to give the limit in distribution of a critical Galton–Watson tree, with finite support, conditioned on having a large width.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference7 articles.
1. Local limits of conditioned Galton–Watson trees: The infinite spine case;Abraham;Electron. J. Prob.,2014
2. Local limits of Galton–Watson trees conditioned on the number of protected nodes
3. Subdiffusive behavior of random walk on a random cluster;Kesten;Ann. Inst. H. Poincaré Prob. Statist.,1986
4. Conditioning Galton–Watson Trees on Large Maximal Outdegree
5. [3] Abraham, R. and Delmas, J. F. (2015). An introduction to Galton–Watson trees and their local limits. Preprint, arXiv:1506.05571.