Limits of random networks

The vision of this proposal is to explore the exciting intersection between combinatorics and probability theory, which has emerged as a crucial area of study in recent years. This innovative field encompasses a wide range of important topics, from the study of random discrete structures and associated stochastic processes, to the analysis of algorithms and their applications. The interplay between these two disciplines holds enormous potential for new discoveries, with implications for fields such as statistical physics, theoretical computer science, and mathematical biology. Research in the area of random combinatorial structures in particular is a broad and dynamic area of study, that explores a variety of different directions. One major focus of investigation is asymptotic counting, which looks at the number of combinatorial structures as their size grows. Another important avenue of research is the examination of the distributional properties of the parameters associated with these structures. This includes the identification of limiting objects, such as those defined by Benjamini and Schramm, or the study of scaling limits.