论文标题
随机有限置信动力学的有限时间界限
Finite Time Bounds for Stochastic Bounded Confidence Dynamics
论文作者
论文摘要
在这个快速和大规模舆论形成的时代，对意见进化的数学理解，也就是意见动力学，具有重要的意义。基于线性图的动力学和有限的置信动力学是社交网络中意见动态的两个流行模型。提出了随机有限的置信度（SBC）意见动力学作为一个通用框架，将这些动态纳入特殊情况，并捕获现实生活中的社会交流中固有的随机性和噪声（错误）。尽管SBC动力学是相当通用和现实的，但其分析更具挑战性。这是因为SBC动力学是非线性和随机性的，并且属于Markov过程的类别，这些过程渐近地漂移和无界跳跃。 SBC动力学的渐近行为在先前的工作中被表征。但是，他们并没有阐明其有限的时间行为，这通常是实践中感兴趣的。我们通过分析两个代理系统和Bistar图的有限时间行为来迈向这个方向，这对于理解一般的多代理动力学至关重要。特别是，我们表明，在导致SBC动力学的渐近稳定性的条件下，两种药物之间的意见差异在零左右。
In this era of fast and large-scale opinion formation, a mathematical understanding of opinion evolution, a.k.a. opinion dynamics, acquires importance. Linear graph-based dynamics and bounded confidence dynamics are the two popular models for opinion dynamics in social networks. Stochastic bounded confidence (SBC) opinion dynamics was proposed as a general framework that incorporates both these dynamics as special cases and also captures the inherent stochasticity and noise (errors) in real-life social exchanges. Although SBC dynamics is quite general and realistic, its analysis is more challenging. This is because SBC dynamics is nonlinear and stochastic, and belongs to the class of Markov processes that have asymptotically zero drift and unbounded jumps. The asymptotic behavior of SBC dynamics was characterized in prior works. However, they do not shed light on its finite-time behavior, which is often of interest in practice. We take a stride in this direction by analyzing the finite-time behavior of a two-agent system and a bistar graph, which are crucial to the understanding of general multi-agent dynamics. In particular, we show that the opinion difference between the two agents is well-concentrated around zero under the conditions that lead to asymptotic stability of the SBC dynamics.
