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Stable Boundaries of Opinion Dynamics in Heterogeneous Spatial Complex Networks.
Mats Bierwirth1, Johannes Lengler1
1Department of Computer Science, ETH Zürich, 8092 Zürich, Switzerland.
Entropy (Basel, Switzerland)
|May 4, 2026
Summary
Opinion dynamics on spatial networks show that distinct opinion groups can stabilize, preventing consensus. This research explains how network structure supports persistent opinion diversity.
Area of Science:
- Complex Systems
- Network Science
- Social Dynamics
Background:
- Classic opinion dynamics often lead to global consensus.
- Geometric Inhomogeneous Random Graphs (GIRGs) model spatial networks.
- Understanding opinion stability in diverse networks is crucial.
Purpose of the Study:
- Investigate opinion dynamics on GIRGs.
- Explain the mechanism of arrested coarsening.
- Provide a mathematical basis for opinion diversity.
Main Methods:
- Simulations of majority-vote dynamics on GIRGs.
- Development of a mean-field model for domain interfaces.
- Rigorous mathematical analysis of the interface profile.
Main Results:
- Localized opinion domains stabilize, preventing consensus.
- Arrested coarsening leads to persistent coexistence of opinions.
- A stable, non-trivial limiting distribution for the interface profile was established.
Conclusions:
- Complex network geometry can support robust opinion diversity.
- Stationary boundaries between opinions explain persistent diversity.
- Findings offer insights into social systems with competing viewpoints.
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