论文
arXiv
SpatialIntelligence
ComplexNetwork
GeoSimulation
中文标题
异质空间复杂网络中意见动态的稳定边界
English Title
Stable Boundaries of Opinion Dynamics in Heterogeneous Spatial Complex Networks
Mats Bierwirth, Johannes Lengler
发布时间
2026/3/10 18:40:09
来源类型
preprint
语言
en
摘要
中文对照

我们研究了在几何非均匀随机图(GIRGs)上的多数投票意见动态,该模型是空间复杂网络的强大表征。与经典粗化动态中通常达成全局共识的情况不同,我们的模拟表明,足够大且局部集中的意见区域不会消失。相反,它们趋于稳定,导致竞争性意见的持续共存。为理解这种被抑制的粗化机制,我们构建并分析了一个两个意见区域界面的可处理均值场模型。我们的主要理论结果在均值场分析中严格证明了界面轮廓存在一个稳定且非平凡的极限分布。这表明意见边界处于静止状态,为复杂网络几何结构如何在社会系统中支持稳健的意见多样性提供了数学解释。

English Original

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.

元数据
arXiv2603.09485v1
来源arXiv
类型论文
抽取状态raw
关键词
SpatialIntelligence
ComplexNetwork
GeoSimulation
cs.SI
physics.soc-ph