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

Romain Abraham (1) , Jean-François Delmas (2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

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.

Mots clés: Galton-Watson; random tree; condensation; non-extinction; branching process

Domaines: Probabilités [math.PR]

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