Conditioning of marked Galton-Watson trees

par Sonia Boulal

jeudi 1 oct. 2026, 14:00 → 15:00 Europe/Paris

Fokko du Cloux (Lyon 1)

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.