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Local limits of conditioned Galton-Watson trees: the infinite spine case.

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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Contributor : Romain Abraham <>
Submitted on : Wednesday, October 16, 2013 - 3:30:34 PM
Last modification on : Friday, May 4, 2018 - 1:17:27 AM
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Romain Abraham, Jean-François Delmas. Local limits of conditioned Galton-Watson trees: the infinite spine case.. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2014, 19, Article 2, pp 1-19. ⟨10.1214/EJP.v19-2747⟩. ⟨hal-00813145v4⟩

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