Title: Scale-free spatial random graphs: local behavior and some deviation problems.
Abstract: In this talk, we will consider the general class of scale-free spatial random graphs, which have emerged as a general tool to model snapshots of real-world networks. In the first part of the talk, we will focus on the local behavior of finite versions of such models and see how to establish a local limit towards a natural infinite version. We will study some consequences of this local convergence. In the second part, we will consider large deviations of the total number of edges in such models and try to figure out the main mechanism driving the large deviations. We will end with many open questions. Based on joint works with Remco van der Hofstad, Pim van der Hoorn, Peter Mörters, and Céline Kerriou.