Séminaire des doctorants Orléans
Sonia Boulal: Penalization of Galton Watson treesSonia Boulal (IDP-Orléans)
Thursday 03 October 2024 10:30 - IDP-Orléans - Salle de séminaire
Résumé :
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.
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