Electronic Journal of Probability

Local limits of conditioned Galton-Watson trees: the condensation case

Romain Abraham and Jean-François Delmas

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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.

Article information

Source
Electron. J. Probab., Volume 19 (2014), paper no. 56, 29 pp.

Dates
Accepted: 27 June 2014
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465065698

Digital Object Identifier
doi:10.1214/EJP.v19-3164

Mathematical Reviews number (MathSciNet)
MR3227065

Zentralblatt MATH identifier
1304.60091

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60B10: Convergence of probability measures

Keywords
Galton-Watson random tree condensation non-extinction branching process

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Abraham, Romain; Delmas, Jean-François. Local limits of conditioned Galton-Watson trees: the condensation case. Electron. J. Probab. 19 (2014), paper no. 56, 29 pp. doi:10.1214/EJP.v19-3164. https://projecteuclid.org/euclid.ejp/1465065698


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References

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