有限连通图上多元Deffuant模型的一致概率
Probability of consensus in the multivariate Deffuant model on finite connected graphs
摘要：
Deffuant模型是一个空间随机模型的动态意见，其中个人位于一个连通图表示社会网络，其特征在于在单位区间内的数字代表他们的意见。该系统根据以下平均过程演化：当且仅当它们的意见之间的距离不超过某个置信阈值时，邻居对以速率1独立地交互，每次交互导致邻居的意见彼此更接近。到目前为止，所有关于这个模型的数学结果都假设个体位于整数上。相比之下，我们研究更现实的情况下，社会网络可以是任何有限的连通图。此外，我们将意见空间扩展到赋范向量空间的任何有界凸子集，其中范数用于测量意见之间的分歧或距离。我们的主要结果给出了一致性概率的下界。有趣的是，我们的证明导致了一个普遍的下界，它取决于置信阈值，意见空间~（凸子集和范数）和初始分布，但不依赖于社会网络的大小或拓扑结构。
英文摘要：
The Deffuant model is a spatial stochastic model for the dynamics of opinions in which individuals are located on a connected graph representing a social network and characterized by a number in the unit interval representing their opinion. The system evolves according to the following averaging procedure: pairs of neighbors interact independently at rate one if and only if the distance between their opinions does not exceed a certain confidence threshold, with each interaction resulting in the neighbors' opinions getting closer to each other. All the mathematical results collected so far about this model assume that the individuals are located on the integers. In contrast, we study the more realistic case where the social network can be any finite connected graph. In addition, we extend the opinion space to any bounded convex subset of a normed vector space where the norm is used to measure the level of disagreement or distance between the opinions. Our main result gives a lower bound for the probability of consensus. Interestingly, our proof leads to a universal lower bound that depends on the confidence threshold, the opinion space~(convex subset and norm) and the initial distribution, but not on the size or the topology of the social network.
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。
