2023/09/09 by Natasa Dragovic, François Baccelli, Dragovic, Natasa +1 · 1 citation
Physics and Astronomy · Social Sciences · #Complex Network Analysis Techniques #Dynamical Systems (math.DS) #Evolutionary Game Theory and Cooperation #FOS: Mathematics #Opinion Dynamics and Social Influence #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2309.04864
openalex publication_date 2023/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a stochastic geometry dynamics inspired by opinion dynamics that captures the essence of modern asymmetric social networks with leaders and followers. Points in the Euclidean space represent opinions, and the leader of an agent is the one with the closest opinion. In this dynamics, each follower updates its opinion by halving the distance to its leader. We demonstrate that this simple dynamics and its iterations exhibit several interesting purely geometric phenomena related to the evolution of leadership and opinion clusters, which resemble those observed in social networks. We also show that when the initial opinions are randomly distributed as a stationary Poisson point process, the spatial frequency of each of these phenomena can be expressed through an integral geometry formula involving semi-algebraic domains. Finally, we analyze numerically the limiting behavior of this follower dynamics. In the Poisson case, the agents fall into two categories: ultimate followers, who continue updating their opinions indefinitely, and ultimate leaders, who adopt a fixed opinion after a finite time. Spatial discrete event simulations support all our findings.