一类具有置信阈值的一般选举模型的极限行为
Limiting behavior for a general class of voter models with confidence threshold
摘要：
本文研究了一般的观点动态的随机空间模型。与选举模型类似，个体位于连通图的顶点集上，并根据邻居的意见以恒定的速率更新自己的意见。然而，与选举模型不同的是，意见集由另一个连通图的顶点集表示，我们称之为意见图：当一个人与邻居互动时，当且仅当他们的意见之间的距离（定义为由意见图引起的图距离）不超过某个置信阈值时，她才会模仿这个邻居。当置信度阈值至少等于意见图的半径时，证明了一维过程是波动的和聚类的，并给出了该过程在有限连通图上的一致性概率的一个普适下界.我们还建立了一个一般的充分条件固定的无限系统的基础上的结构的意见图，我们然后显着改善意见图的距离正则。我们的一般结果是用来了解系统的动态的各种例子的意见图：路径和恒星，这是不是距离定期，周期，超立方体和五个柏拉图固体，这是距离定期。
英文摘要：
This article is concerned with a general class of stochastic spatial models for the dynamics of opinions. Like in the voter model, individuals are located on the vertex set of a connected graph and update their opinion at a constant rate based on the opinion of their neighbors. However, unlike in the voter model, the set of opinions is represented by the set of vertices of another connected graph that we call the opinion graph: when an individual interacts with a neighbor, she imitates this neighbor if and only if the distance between their opinions, defined as the graph distance induced by the opinion graph, does not exceed a certain confidence threshold. When the confidence threshold is at least equal to the radius of the opinion graph, we prove that the one-dimensional process fluctuates and clusters and give a universal lower bound for the probability of consensus of the process on finite connected graphs. We also establish a general sufficient condition for fixation of the infinite system based on the structure of the opinion graph, which we then significantly improve for opinion graphs which are distance-regular. Our general results are used to understand the dynamics of the system for various examples of opinion graphs: paths and stars, which are not distance-regular, and cycles, hypercubes and the five Platonic solids, which are distance-regular.
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。
