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

Romain Abraham (Université d'Orléans)
Jean-François Delmas (Université Paris-Est)

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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Pages: 1-29

Publication Date: June 27, 2014

DOI: 10.1214/EJP.v19-3164

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