Title: “From the minimal spanning tree problem to the Erdős-Rényi graph”.

Abstract: As an introduction to the Erdős- Rényi graph, I will present a possibly original approach to the famous problem initiated by Alan Frieze of the asymptotic weight of the minimal spanning tree inside a complete graph whose edges are iid distributed. The problem of fluctuations of this weight will  lead to some natural issues on the Erdős-Rényi graph, among them the limit of the process of the fluctuations of the size of the giant component, as the connecting  parameter varies.
(Joint work with Gabriel Faraud and Sophie Lemaire)