Stochastic Models of Higher-Order Networks

Many networks involve interactions among groups, rather than only pairs of entities. During my PhD at Aarhus University, I developed spatial and dynamic models of these higher-order relationships with collaborators. We established limit theorems for network statistics, including degree distributions, edge counts, and topological characteristics. I implemented high-performance Monte Carlo algorithms in Python and C++ to investigate finite-sample behavior and assess theoretical predictions. Fitting models and conducting hypothesis tests on scientific collaboration networks connected the mathematical results to empirical data. The research is documented in my thesis, work on higher-order network topology, and dynamic hypergraphs, alongside public simulation software and a collaboration dataset.