Modul: MAT971 Stochastische Prozesse

## Fragmentation of trees and drifted excursions

Talk by Dr. Paul Thévenin

Speaker invited by: Prof. Dr. Jean Bertoin

**Date:** 19.10.22 **Time:** 17.15 - 18.15 **Room:** ETH HG G 19.1

The fragmentation of a tree is a process which consists in cutting the tree at random points, thus splitting it into smaller connected components as time passes. In the case of the so-called Brownian tree, it turns out that the sizes of these subtrees, known as the Aldous-Pitman fragmentation process, have the same distribution as the lengths of the excursions over its current infimum of a linearly drifted Brownian excursion, as proved by Bertoin.

We provide a natural coupling between these two objects. To this end, we make use of the so-called cut-tree of the Brownian tree, which can be seen as the genealogical tree of the fragmentation process. Joint work with Igor Kortchemski.