Geometric random graphs with a scale-free degree distribution have been the go-to random graph in the network science community to model many real-life networks. In this talk, after introducing the model, and discussing some previous work on them, I will focus on the problem of condensation effects in such models. More specifically, we look at upper tail large deviations of the total number of edges in such graphs and show that the excess number of edges leading to the large deviation event, come from a condensation effect in the underlying degree distribution. This is in sharp contrast with the condensation effect in the `classical' random geometric graph observed by the authors of https://arxiv.org/abs/1401.7577 , where the condensation instead takes place in the underlying space. This difference is due to the scale-free nature of our model. Here, because of the high variability in the degrees, the randomness of the degree distribution overpowers the randomness of the underlying vertex locations, which gives rise to degree condensates - vertices with super high degrees contributing the excess number of edges in the large deviation event. Based on joint ongoing work with Remco van der Hofstad, Pim van der Hoorn, Céline Kerriou and Peter Mörters.
