Abstract : In this talk, we present a recently introduced family of phylogenetic networkbalance indices. These indices $(H_alpha)_{alpha geqslant 0}$ are based on the statistical properties of random walks on such networks, similarly as a possible definition of the $B_2$ index. First, we show how the distribution of~$H_alpha$ can be studied for several classic models of random trees, such as the Yule, PDA and Galton–Watson models. Next, we demonstrate how local limits can be used to study the asymptotic behavior of $H_alpha(G_n)$ as the size of $G_n$ goes to infinity, with a focus on a class of models of random phylogenetic networks known as blowups of Galton–Watson trees. This is a joint work with F. Bienvenu and J.-J. <a href="http://Duchamps.

https://indico.math.cnrs.fr/event/17423/ » target= »_blank » title= »Duchamps.

https://indico.math.cnrs.fr/event/17423/ »>Duchamps.

https://indico.math.cnrs.fr/event/17423/