Probabilistic methods for complex discrete structures

Large discrete structures are ubiquitous in the modern world, and are modelled using random graphs orhypergraphs. However, existing analysis techniques fall short of the generality required to capture real-worldapplications, due to the size, irregularity and structural constraints of these networks. This project aims to build onrecent breakthroughs to develop new theoretical tools to overcome these barriers. Expected outcomes includeenumeration formulae and new probabilistic estimates for pattern appearances in complex discrete structures. The explicit formulae and practical algorithms produced by our project will benefit researchers who model realworlddiscrete systems using graphs or hypergraphs.