Scaling limits of a random graph: critical configuration model with power-law degrees

schedule le lundi 26 novembre 2018 de 17h00 à 18h00

Organisé par : F. Coppini, B. Dembin

Intervenant : Guillaume Conchon--Kerjan (LPSM)
Lieu : Salle 1016, Bâtiment Sophie Germain, Paris 7 Diderot

Sujet : Scaling limits of a random graph: critical configuration model with power-law degrees

Résumé :

A configuration model is a random graph built as follows: one first chooses the degrees of each vertex (in a deterministic or random way), then one chooses uniformly at random a matching of those vertices that respects the degree sequence. In this talk, we focus on a setting in which the degrees have a "critical" law, that is, vertices have (in some sense) just less than two neighbours in average. We will see that if the number N of vertices goes to infinity, the largest connected components, seen as metric spaces (with the usual graph distance) and properly rescaled w.r.t. N, have a limiting shape close to the alpha-stable random tree. A key tool for studying the graph is an exploration process that encodes information while walking on its components: it turns out that it has a scaling limit, namely a slightly modified stable Lévy process.