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

Romain Abraham; Jean-Francois Delmas

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arXiv · 1311.6683

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

Romain Abraham·Jean-Francois Delmas

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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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Romain Abraham, Jean-Francois Delmas. 2013-11-26. Local limits of conditioned Galton-Watson trees II: the condensation case. https://arxiv.org/abs/1311.6683

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