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

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.
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https://hal.archives-ouvertes.fr/hal-00909604
Contributor : Romain Abraham <>
Submitted on : Tuesday, November 26, 2013 - 3:14:07 PM
Last modification on : Friday, May 4, 2018 - 1:17:28 AM
Document(s) archivé(s) le : Thursday, February 27, 2014 - 10:10:09 AM

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  • HAL Id : hal-00909604, version 1
  • ARXIV : 1311.6683

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Romain Abraham, Jean-François Delmas. Local limits of conditioned Galton-Watson trees: the condensation case. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2014, 56, Article 56, pp 1-29. ⟨hal-00909604⟩

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