Sonia Boulal: Penalization of Galton Watson trees

par Mme Sonia Boulal (IDP-Orléans)

jeudi 3 oct. 2024, 10:30 → 11:30 Europe/Paris

Salle de séminaire (IDP-Orléans)

In this presentation, we are interested in Galton-Watson trees whose particularity is that each node can be marked with a probability depending on its number of children, independently of the other nodes. Subsequently, using a method called penalization we favor trees with a small number of marks. More precisely, this method makes it possible to obtain martingales which are in our case functions of $M_n$, the number of marks up to generation $n-1$ and $Z_n$ the number of individuals at generation $n$. These martingales being positive and with mean 1, we can then define new probabilities under which we study the laws of marked trees.