Electronic Journal of Probability
- Electron. J. Probab.
- Volume 19 (2014), paper no. 2, 19 pp.
Local limits of conditioned Galton-Watson trees: the infinite spine case
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.
Electron. J. Probab., Volume 19 (2014), paper no. 2, 19 pp.
Accepted: 3 January 2014
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
This work is licensed under a Creative Commons Attribution 3.0 License.
Abraham, Romain; Delmas, Jean-François. Local limits of conditioned Galton-Watson trees: the infinite spine case. Electron. J. Probab. 19 (2014), paper no. 2, 19 pp. doi:10.1214/EJP.v19-2747. https://projecteuclid.org/euclid.ejp/1465065644