### Upper bounds for the largest component in critical inhomogeneous random graphs

Probability Seminar

4th November 2022, 3:30 pm – 4:30 pm

Fry Building, 2.04

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. Next, I will consider the Norrous-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.

Finally, I will present the results of a joint work with Umberto De Ambroggio where we analyse the order of the maximal component of this model, in the critical regimen. We use probabilistic arguments based on martingales and adapt some ideas originally introduced by Nachmias and Peres (2010).

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