Title: Abstract Formulation of Mean-Field Models and Propagation of Chaos Show Chinese title

Title: 摘要 平均场模型的表述与混沌传播

Abstract: In this work, we formulate an abstract framework to study mean-field systems. In contrast to most approaches in the available literature which primarily rely on the analysis of SDEs, ours is based on optimal transport and semigroup theory. This allows for the inclusion of a wider range of mean-field particle systems within a unified structure. This new approach involves: (1) constructing an abstract framework using semigroups and generators; (2) formulating a corresponding mean-field evolution problem, and proving its well-posedness; (3) demonstrating the propagation of chaos for a class of N-particle systems associated with the mean-field model. Our results are readily applicable to various mean-field models. To demonstrate this, we apply our findings to obtain a new result for Levy-type mean-field systems, which encompass the McKean-Vlasov diffusion. Show Chinese abstract

Abstract: 在这项工作中，我们提出了一个抽象框架来研究平均场系统。与现有文献中主要依赖随机微分方程分析的方法不同，我们的方法基于最优传输和半群理论。这使得能够在统一结构中包含更广泛的平均场粒子系统。这种方法包括：(1) 使用半群和生成元构建一个抽象框架；(2) 构造相应的平均场演化问题，并证明其适定性；(3) 展示与平均场模型相关的N粒子系统类的混沌传播。我们的结果可直接应用于各种平均场模型。为了证明这一点，我们将这些结果应用于获得一种新的利维型平均场系统的结果，该系统包括麦考恩-弗拉索夫扩散。