Résumé : Many processes involving growing trees/graphs are adding a small amount of nodes/edges at each step. Such models often exhibit statistics (like the degree distribution) which are not compatible with the ones observed e.g. in social networks. Is there a natural mathematical model which possess this fast growing rate feature? To this aim, we consider a new family of trees (introduced by Mahmoud): the exponential recursive trees. At each step, one adds (with probability $p$) a new child to each node of the tree. In this talk, we establish typical properties concerning the evolution at time $n$ of such a tree: its size, its number of leaves at depth $d$, its internal path length, its number of protected nodes. Using martingale theory, we give results on average or in $L^1$ and some of the corresponding limit distributions (characterized by their moments). We end with some open problems.

 [Slides.pdf] [vidéo]

Dernière modification : Thursday 21 November 2024

Contact pour cette page : Cyril.Banderier at lipn.univ-paris13.fr