论文标题
八卦意见动态与社区结构的短暂行为
Transient Behavior of Gossip Opinion Dynamics with Community Structure
论文作者
论文摘要
我们研究了八卦意见动力学的瞬态行为,其中代理在加权图上与两个社区随机相互作用。社区内的边缘的权重与社区之间的边缘权重不同。我们首先在代理人意见的第二刻中得出上限。使用这种界限,我们获得了上限,因为很大一部分代理的意见接近平均水平。结果暗示了该过程的瞬态行为的相位过渡:当社区内的边缘权重大于社区和普通人和顽固的代理之间的社区中的边缘权重时,同一社区中的大多数代理人都在此过程的早期阶段,在该社区的平均意见附近。但是,如果社区内和社区间权重之间的差异很小,那么大多数代理商在早期阶段就将意见与每个人的平均意见接近。相比之下,当顽固的特工的影响很大时,代理商的意见很快就会稳定在稳定状态下。然后,我们进行数值实验以验证理论结果。与大多数观点动态文献中的传统渐近分析不同,本文是顽固的代理人和社区结构在意见进化的初始阶段的影响。
We study transient behavior of gossip opinion dynamics, in which agents randomly interact pairwise over a weighted graph with two communities. Edges within a community have identical weights different from edge weights between communities. We first derive an upper bound for the second moment of agent opinions. Using this bound, we obtain upper bounds for probability that a large proportion of agents have opinions close to average ones. The results imply a phase transition of transient behavior of the process: When edge weights within communities are larger than those between communities and those between regular and stubborn agents, most agents in the same community hold opinions close to the average opinion of that community with large probability, at an early stage of the process. However, if the difference between intra- and inter-community weights is small, most of the agents instead hold opinions close to everyone's average opinion at the early stage. In contrast, when the influence of stubborn agents is large, agent opinions settle quickly to steady state. We then conduct numerical experiments to validate the theoretical results. Different from traditional asymptotic analysis in most opinion dynamics literature, the paper characterizes the influences of stubborn agents and community structure on the initial phase of the opinion evolution.