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.