Sannolikhet, statistik och kombinatorik: The pruning process on real trees

Abstract: Aldous and Pitman introduced a tree-valued Markov chain by pruning off more and more sub-trees along the edges of a Galton-Watson tree.  More generally, Abraham and Delmas defined a non-uniform pruning process on the branch points of a Galton-Watson tree. In the same spirit, some authors have considered the continuum tree analogues (i.e. Lévy trees) of pruning dynamics. The aim of this talk is to present a topology which allows to link the discrete and continuum tree-valued dynamics in order to show an invariance principle for the pruning process of Galton-Watson trees. Roughly speaking,  we construct the pruning process on the space of so-called bi-measure trees, which are metric measure spaces with an additional pruning measure. 

This is joint work with Anita Winter from the University of Duisburg-Essen.