标题： 带有置信阈值的舆论动力学：一种替代阿克洛德模型的方法 显示英文标题

标题： Opinion dynamics with confidence threshold: an alternative to the Axelrod model

摘要： 选民模型和Axelrod模型是描述网络上意见传播的两种主要随机过程。 前者包括社会影响，即个体在相互作用时倾向于变得更加相似，而后者还考虑了同质性，即倾向于与更加相似的个体进行更频繁的互动。 在过去十年中，Axelrod模型已经通过数值模拟进行了广泛研究。 相比之下，我们给出了一个与Axelrod模型密切相关且结合了社会影响和信任阈值的选民模型的推广的严格分析结果，这种信任阈值在某种程度上类似于同质性。 网络中的每个顶点，由一个有限连通图表示，具有一个意见，并可能与其相邻顶点进行交互。 像选民模型一样，一次交互会导致两个交互顶点达成一致——社会影响——但与选民模型不同的是，只有当顶点的意见处于一定距离内时才会发生交互——信任阈值。 在确定性的静态方法中，我们首先给出了网络能够支持的最大意见数的下界和上界，该数值作为信任阈值和图的各种特征的函数。 然后，在概率动态方法中，研究了从随机配置开始的随机过程在平衡状态下共存的意见数量... 显示英文摘要

摘要： The voter model and the Axelrod model are two of the main stochastic processes that describe the spread of opinions on networks. The former includes social influence, the tendency of individuals to become more similar when they interact, while the latter also accounts for homophily, the tendency to interact more frequently with individuals which are more similar. The Axelrod model has been extensively studied during the past ten years based on numerical simulations. In contrast, we give rigorous analytical results for a generalization of the voter model that is closely related to the Axelrod model as it combines social influence and confidence threshold, which is modeled somewhat similarly to homophily. Each vertex of the network, represented by a finite connected graph, is characterized by an opinion and may interact with its adjacent vertices. Like the voter model, an interaction results in an agreement between both interacting vertices -- social influence -- but unlike the voter model, an interaction takes place if and only if the vertices' opinions are within a certain distance -- confidence threshold. In a deterministic static approach, we first give lower and upper bounds for the maximum number of opinions that can be supported by the network as a function of the confidence threshold and various characteristics of the graph. The number of opinions coexisting at equilibrium is then investigated in a probabilistic dynamic approach for the stochastic process starting from a random configuration ...