Speaker: 洪伟，江苏师范大学

Inviter: 随机分析研究中心

Title: Recent progress on mean-field stochastic PDEs

Language: Chinese

Time & Venue: 2026.05.29 15:00-16:00 南楼N613

Abstract: In this talk, I will introduce recent progress on the mean field stochastic PDEs with pseudo-monotone kernels. Firstly, we prove the qualitative convergence (in certain Wasserstein metric) of the empirical laws of infinite-dimensional interacting systems to the law of solutions of mean field stochastic PDEs in the variational framework, as the number of particles tends to infinity. Secondly, we establish the quantitative estimates for dimension-free propagation of chaos in a p-uniformly convex Banach space. This reveals a new phenomenon: the convergence rate of propagation of chaos for infinite-dimensional interacting particle systems inherently depends on the modulus of convexity of the underlying solution space.

The main challenge lies in addressing the inherent interplay between the high nonlinearity of infinite- dimensional operators and the non-local effect of coeﬀicients that depend on the measure. In particular, we do not need to assume any exponential moment control condition of solutions, which extends the range of the applicability of our results. As applications, we first study a class of finite-dimensional interacting particle systems with polynomial kernels, such as Ensemble Kalman Sampler and stochastic Stein variational gradient descent, which are commonly encountered in machine learning. Subsequently, we present several illustrative examples of infinite-dimensional interacting systems, including stochastic Allen-Cahn equations and Lagrangian averaged Navier-Stokes equations.