Stable Boundaries of Opinion Dynamics in Heterogeneous Spatial Complex Networks
Abstract
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.
Keywords
Cite
@article{arxiv.2603.09485,
title = {Stable Boundaries of Opinion Dynamics in Heterogeneous Spatial Complex Networks},
author = {Mats Bierwirth and Johannes Lengler},
journal= {arXiv preprint arXiv:2603.09485},
year = {2026}
}
Comments
28 pages, 3 figures. Presented at the 14th International Conference on Complex Networks and their Applications (Binghamton, NY, USA). Submitted to Entropy