Mean-field theory on structured netowrks: around propagation of chaos, coupling and marginal laws
发布时间：2025年10月28日
浏览次数：75
发布者: Qiuye Huang
主讲人： Datong Zhou (Sorbonne University)
活动时间： 从 2025-10-30 16:10 到 17:10
场地： 北京国际数学研究中心，全斋全29教室
Abstract:
In the 21st century, the applications of mean-field theory have expanded dramatically beyond its origins in statistical physics, but the remarkable success of this framework across diverse fields hinges on a core "exchangeability" assumption: the constituent "particles" - be they birds, agents, or neurons - are treated as indistinguishable. However, many critical models at the frontier of modern science are defined by their lack of such exchangeability.
This work establishes a rigorous theory for non-exchangeable mean-field limits, extending the theory to particle systems where interactions are governed by a highly structured graph (e.g. the synaptic connections of neurons). This reveals a natural unification between concepts from probability/analysis and graph limiting theory. This unification is established from two perspectives:1. As a novel distance combining optimal transport of particles with graph alignment;
2. As a composition of the marginal distributions of particles and graph homomorphism densities.
