Derivation of macroscopic equations for interacting diffusions with singular kernels Online: attendMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

The mean-field problem for interacting diffusions aims to derive a macroscopic continuum model to approximate the particle system when the number of particles is large. In this talk, we improve the mean-field convergence for interacting diffusions in two directions. The first part is to study the central limit theorem for interacting diffusions, which provides a better continuum approximation than the mean-field convergence. The second part is to study the mean-field problem for interacting diffusions with inhomogeneous interactions, i.e., the interactions are weighted, therefore these particles are not exchangeable. For both topics, our results apply to the stochastic vortex model related to the 2D Navier-Stokes equation. This talk is based on joint work with Zhenfu Wang (Peking University) and Rongchan Zhu (Beijing Institute of Technology).