第50回 北大MMCセミナー

We study the many-particle limit of an interacting particle system. The velocities of the particles are described by a non-linear function which depends on all particle positions. The resulting system of first-order ODEs has a gradient flow structure with respect to an energy functional E_{n}, where n is the number of particles. Our first main result states Γ- convergence of the energy functionals E_{n} as n → ∞. The Γ- limit E is defined on the space of measures, equipped with the 2-Wasserstein topology. These measures represent the particle density. Our second result guarantees the convergence of the related gradient flows.