Stable Boundaries of Opinion Dynamics in Heterogeneous Spatial Complex Networks
This provides a mathematical explanation for how complex network geometry can support robust opinion diversity in social systems, addressing a problem in social dynamics modeling.
The paper investigates majority-vote opinion dynamics on Geometric Inhomogeneous Random Graphs (GIRGs), finding that large, localized opinion domains stabilize instead of disappearing, leading to persistent coexistence of competing opinions. The main theoretical result rigorously establishes a stable, non-trivial limiting distribution for the interface profile in a mean-field analysis, demonstrating that boundaries between opinions are stationary.
We investigate majority-vote opinion dynamics on Geometric Inhomogeneous Random Graphs (GIRGs), a powerful model for spatial complex networks. In contrast to classic coarsening dynamics where a single opinion typically achieves global consensus, our simulations reveal that sufficiently large, localized opinion domains do not disappear. Instead, they stabilize, leading to a persistent coexistence of competing opinions. To understand the mechanism behind this arrested coarsening, we develop and analyze a tractable mean-field model of the interface between two opinion domains. Our main theoretical result rigorously establishes the existence of a stable, non-trivial limiting distribution for the interface profile in a mean-field analysis. This demonstrates that the boundary between opinions is stationary, providing a mathematical explanation for how complex network geometry can support robust opinion diversity in social systems.