Speaker: 郭书晨博士，牛津大学

Title: Quantitative propagation of chaos for multi-species moderately interacting particle systems with attractive Coulomb potentials

Language: Chinese

Time & Venue: 2024.10.24 16:00-17:00 ZOOM会议3541437366 密码：123456

Abstract: We derive a class of multi-species aggregation-diffusion systems from stochastic interacting particle systems via relative entropy method. We generalise the framework of propagation of chaos to multi-component cases, and get the quantitative $L^1$-convergence result by adopting moderately interacting particle systems without further cut-off. It holds global-in-time since we establish the well-posedness of aggregation-diffusion systems up to any time $T>0$ under a sufficient smallness condition on the initial data. To obtain the main result, we estimate the relative entropy between the joint distribution of the particle system and a PDE system at the intermediate level, then the relative entropy between the intermediate PDEs and the limiting aggregation-diffusion system. The core of the first step is to show convergence in probability by stopping time argument, while the second step is done by evaluating a combination of relative entropy and $L^2$-distance. Our method is robust enough that we do not need to pose assumptions on the interaction matrix, and we can handle attractive or repulsive interaction potentials up to the Coulomb singularity, which is the most physical case.