Title: Dynamic Erdős-Rényi graphs,
Abstract: We propose two classes of dynamic versions of the classical Erdős-Rényi
graph: one in which the transition rates are governed by an external regime
process, and one in which the transition rates are periodically resampled. For
both models we consider the evolution of the number of edges present, with
explicit results for the corresponding moments, functional central limit
theorems and large deviations asymptotics.