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arXiv 2603.09485cs.SIphysics.soc-ph
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异质空间复杂网络中意见动态的稳定边界

Stable Boundaries of Opinion Dynamics in Heterogeneous Spatial Complex Networks

ETH Zürich(苏黎世联邦理工学院)

Mats Bierwirth, Johannes Lengler

AI总结:

研究异质空间复杂网络中意见动态的稳定边界,揭示了局部意见域在竞争中持久共存的机制。

摘要:

我们研究了在几何非均匀随机图(GIRGs)上多数投票意见动态,这是一种强大的空间复杂网络模型。与经典粗化动态不同,其中一种意见通常达到全球共识,我们的模拟发现,足够大的局部意见域不会消失。相反,它们会稳定下来,导致竞争意见的持久共存。为了理解这一停滞粗化背后机制,我们开发并分析了两个意见域之间的可处理均场模型。我们的主要理论结果严格证明了在均场分析中界面轮廓的稳定、非平凡极限分布的存在。这表明意见边界是静态的,为复杂网络几何如何在社会系统中支持稳健意见多样性提供了数学解释。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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