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arXiv · 2603.09485

Stable Boundaries of Opinion Dynamics in Heterogeneous Spatial Complex Networks

Mats Bierwirth·Johannes Lengler
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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.

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Mats Bierwirth, Johannes Lengler. 2026-03-10. Stable Boundaries of Opinion Dynamics in Heterogeneous Spatial Complex Networks. https://arxiv.org/abs/2603.09485

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