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2014 Local limits of conditioned Galton-Watson trees: the infinite spine case
Romain Abraham, Jean-François Delmas
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Electron. J. Probab. 19: 1-19 (2014). DOI: 10.1214/EJP.v19-2747

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.

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Romain Abraham. Jean-François Delmas. "Local limits of conditioned Galton-Watson trees: the infinite spine case." Electron. J. Probab. 19 1 - 19, 2014. https://doi.org/10.1214/EJP.v19-2747

Information

Accepted: 3 January 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1285.60085
MathSciNet: MR3164755
Digital Object Identifier: 10.1214/EJP.v19-2747

Subjects:
Primary: 60J80

JOURNAL ARTICLE
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