This seminar will be held online.
Title: Critical behaviour in inhomogeneous random graphs, with martingales
Abstract: Numerous random graphs inspired in real networks are inhomogeneous in the sense that not all vertices have the same characteristics, which may influence the connection probabilities between pairs of vertices. In this talk, I will start by presenting the most known inhomogeneous random graph models and some of their properties. Next, I will consider the Norrous and Reittu random graph model where edges are present independently, but edge probabilities are moderated by vertex weights. On the critical regime this model is studied by van der Hofstad (2012) using a branching process approximation. We study the same regimen and provide simpler upper bounds for the probability of observing unusually large maximal components with respect to those available in the literature. We do this by adapting a martingale method introduced by Nachmias and Peres (2010). This is a joint work with Umberto De Ambroggio.