Zoom link: https://cornell.zoom.us/j/98013630709?pwd=UlhJVTlMWnUwQysvNTdMMS9NQmtsZz09

Abstract: Exponential random graph models (ERGMs) are parametric families of distributions on graphs that are widely applied in the social sciences. They can be viewed as tilts of the Erdős–Rényi model by a Gibbs weight that depends on counts of small subgraphs such as triangles. While they have some appealing features for doing statistics, sampling from these distributions is challenging in many parameter regimes; in some other regimes, typical samples are indistinguishable from the Erdős–Rényi model, or may even "degenerate" to an almost-empty or almost-full graph. Following an idea of Lubetzky and Zhao for the dense case, we show how to cure the degeneracy phenomenon for sparse ERGMs. We further use recent advances in nonlinear large deviations theory for random hypergraphs to establish the typical macroscopic structure of sparse ERGMs in the ferromagnetic parameter regime. Based on joint works with Amir Dembo and Huy Tuan Pham.