Speaker
Sonia BOULAL
(Institut Denis Poisson, Université d’Orléans)
Description
We consider a Galton–Watson tree in which each node is independently marked, with a probability that depends on its number of offspring.
We give a complete picture of the local convergence of critical or subcritical marked Galton–Watson trees, conditioned on having a large number of marks.
In certain cases, the limit is a randomly marked tree with an infinite spine, known as the marked Kesten tree. In other cases, the local limit is a randomly marked tree with a node having infinitely many children. This corresponds to the so-called marked condensation phenomenon.
Joint work with Romain Abraham and Pierre Debs.