连续意见动力学系统的标度极限
Scaling limits for continuous opinion dynamics systems
摘要：
分析了随机连续意见动力学系统（也称为流言模型）的标度极限。在这样的模型中，代理更新他们的向量值的意见，以凸组合（可能代理和意见相关）的当前值和另一个观察到的代理。结果表明，在大代理总体规模的限制，经验意见密度集中，在指数概率率，周围的概率测度值的常微分方程描述系统的平均场动力学的解决方案。研究了相应的初值问题的性质。解的渐近行为进行了分析，有界置信度的意见动态，并在一个异构的有影响力的环境的存在下。
英文摘要：
Scaling limits are analyzed for stochastic continuous opinion dynamics systems, also known as gossip models. In such models, agents update their vector-valued opinion to a convex combination (possibly agent- and opinion-dependent) of their current value and that of another observed agent. It is shown that, in the limit of large agent population size, the empirical opinion density concentrates, at an exponential probability rate, around the solution of a probability-measure-valued ordinary differential equation describing the system's mean-field dynamics. Properties of the associated initial value problem are studied. The asymptotic behavior of the solution is analyzed for bounded-confidence opinion dynamics, and in the presence of an heterogeneous influential environment.
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