Replica mean-field limits of fragmentation-interaction-aggregation processes

Résumé :
Network dynamics with point-process-based interactions are of paramount modeling interest. Unfortunately, most relevant dynamics involve complex graphs of interactions for which an exact computational treatment is impossible. To circumvent this difficulty, the replica-mean-field approach focuses on randomly interacting replicas of the networks of interest. In the limit of an infinite number of replicas, these networks become analytically tractable under the so-called "Poisson Hypothesis". However, in most applications, this hypothesis is only conjectured. In this talk, we will present results on the validity of the Poisson Hypothesis in a general class of discrete-time, point-process-based dynamics we call fragmentation-interaction-aggregation processes.