A new model for random discrete structures: distributions, counting and sampling

Random discrete structures are used in countless applications across science for modelling complex systems. We will study a new, very general model of random discrete structures which encapsulates both random networks and random matrices. We will develop general tools for working with this model, thereby unlocking the model for use by practitioners in areas such as physics, biology, statistics and cryptography. The questions that we will tackle are fundamental problems in probability, and include as special cases the analysis of subgraph distribution in models of random networks, and the joint distribution of entries of contingency tables, which are important in statistics.