Séminaire Jeunes chercheurs (Sonia Boulal, jeudi 12 décembre 2024)

La prochaine séance du séminaire Jeunes chercheurs du CEREMADE aura lieu le jeudi 12 décembre 2024 à 17h en salle A707. Nous aurons le plaisir d'écouter Sonia Boulal (Institut Denis Poisson, Université d'Orléans), qui nous parlera de

Penalization of Galton Watson tree with marked vertices

Abstract
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 large 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 $n-1$. These martingales being positive and with mean 1, we can then define new probabilities under which we study the laws of marked trees.