具有社区结构的非稀疏网络上的观点动力学
Opinion dynamics on non-sparse networks with community structure
AI总结：
本文研究具有社区结构的有向网络上观点演化的平均场近似，证明在平均度趋于无穷时观点过程对任意边密度都集中且具有混沌传播性质，并给出可用于量化共识与极化的显式平均场公式。
摘要：
我们研究具有社区结构的有向网络上观点的演化。个体基于其邻居观点的加权平均、自身先前的观点以及外部媒体信号同步更新自己的观点。我们的模型类似于流行的Friedkin-Johnsen模型，并且能够纳入诸如固执性、确认偏误、选择性接触和多个话题等因素，这些因素被认为在观点形成中起着重要作用。我们的主要结果表明，在大图极限下，只要平均度增长到无穷大，对于任意边密度水平，观点过程都集中在其平均场近似附近。此外，我们证明了观点过程表现出混沌传播。我们还给出了关于单个顶点轨迹和观点过程平稳版本的结果，并证明了时间极限与网络规模极限可交换。该平均场近似是显式的，可用于量化共识和极化。
英文摘要：
We study the evolution of opinions on a directed network with community structure. Individuals update their opinions synchronously based on a weighted average of their neighbors' opinions, their own previous opinions, and external media signals. Our model is akin to the popular Friedkin-Johnsen model, and is able to incorporate factors such as stubbornness, confirmation bias, selective exposure, and multiple topics, which are believed to play an important role in the formation of opinions. Our main result shows that, in the large graph limit, the opinion process concentrates around its mean-field approximation for any level of edge density, provided the average degree grows to infinity. Moreover, we show that the opinion process exhibits propagation of chaos. We also give results for the trajectories of individual vertices and the stationary version of the opinion process, and prove that the limits in time and in the size of the network commute. The mean-field approximation is explicit and can be used to quantify consensus and polarization.
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