Description
This series of lectures explores the fundamental concepts of Mean Field Kinetic Equations, emphasizing both theoretical foundations and practical applications. We begin by examining several classical examples of mean field models, illustrating their relevance across various physical systems. Subsequently, we introduce a comprehensive formalism for the mean field limit within classical mechanics, unifying the diverse models discussed. A key tool employed throughout the analysis is the Monge-Kantorovich distance, which serves as a convenient measure for investigating the stability of the mean field characteristic flow. Central to our approach is Dobrushin's stability theorem, which provides a rigorous framework for establishing the stability of the flow concerning initial conditions in phase space and initial distributions. We demonstrate that the mean field limit of the N-particle system naturally follows from Dobrushin's stability results. Additionally, we utilize this technique to perform numerical analysis of particle methods, offering insights into their stability and convergence properties in the context of mean field dynamics.