Fast Consensus and Metastability in a Highly Polarized Social Network

A polarized social network is modeled as a system of interacting marked point processes with memory of variable length. Each point process indicates the successive times in which a social actor expresses a "favorable" or "contrary" opinion. After expressing an opinion, the social pressure on the actor is reset to 0, waiting for the group's reaction. The orientation and the rate at which an actor expresses an opinion is influenced by the social pressure exerted on it, modulated by a polarization coefficient. We prove that the network reaches an instantaneous but metastable consensus, when the polarization coefficient diverges.