Modul: MAT971 Stochastische Prozesse

## Additive functionals of large Bienaymé-Galton-Watson trees

Talk by Michel Nassif

Speaker invited by: Prof. Dr. Jean Bertoin

**Date:** 27.04.22 **Time:** 17.15 - 18.15 **Room:** Y27H12

We study the scaling limits of general additive functionals on size-conditioned Bienaymé-Galton-Watson trees. Many usual indices can be written in that form, e.g. the total path length, the Wiener index, and Shao and Sokal’s B1 index. We assume that the offspring distribution is critical with finite or infinite variance. We express the limit as a functional of the stable Lévy tree and study some of its properties. We also describe a phase transition when the toll function depends only on the size and the height of the tree.