Modul: MAT971 Stochastische Prozesse

## Growth-fragmentation processes in Brownian motion indexed by the Brownian tree

Armand Riera talk

Speaker invited by: Prof. Dr. Jean Bertoin

**Date:** 06.03.19 **Time:** 17.15 - 19.00 **Room:** Y27H12

Brownian motion indexed by the Brownian tree is the continuous analog of a random walk indexed by a critical Galton-Watson tree (with finite variance).
It is directly related to the Super-Brownian motion and more surprisingly with Brownian geometry.

The goal of this talk is to present the positive excursion theory of Brownian motion indexed by the Brownian tree and to show that
the genealogy of positive excursions is coded by a well-identified growth-fragmentation process. In the context of Brownian geometry, this means
that if we slice a free Brownian disk at heights the same growth-fragmentation process encodes the perimeter of the resulting connected components.
These connected components evolve, conditionally to their perimeters, as independent Brownian disks.

This talk is based on joint work with Jean-François Le Gall.