文章基本信息

标题：Limiting behavior for a general class of voter models with confidence threshold
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作者：Nicolas Lanchier ; Stylianos Scarlatos
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2017
卷号：XIV
页码：63-92
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：This article is concerned with a general class of stochastic spatial modelsfor the dynamics of opinions. Like in the one-dimensional voter model, individualsare located on the integers and update their opinion at a constant rate based onthe opinion of their neighbors. However, unlike in the voter model, the set ofopinions is represented by the set of vertices of a finite connected graph that wecall the opinion graph: when an individual interacts with a neighbor, she imitatesthis neighbor if and only if the distance between their opinions, defined as thegraph distance induced by the opinion graph, does not exceed a certain confidencethreshold. Our first result shows that, when the confidence threshold is at leastequal to the radius of the opinion graph, the process fluctuates and clusters. Wealso establish a general sufficient condition for fixation of the process based on thestructure of the opinion graph, which we then significantly improve for opiniongraphs which are distance-regular. Our general results are used to understand thedynamics 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.
关键词：Interacting particle systems; voter model; opinion dynamics; confi-;dence threshold; annihilating random walks; fluctuation; fixation; distance-regular graphs.