Size of chaos for Gibbs measures of mean field interacting diffusions

Abstract

We investigate Gibbs measures for diffusive particles interacting through a two-body mean field energy. By identifying a gradient structure for the conditional law, we derive sharp bounds on the size of chaos, providing a quantitative characterization of particle independence. To handle interaction forces that are unbounded at infinity, we study the concentration of measure phenomenon for Gibbs measures via a defective Talagrand inequality, which may hold independent interest. Our approach provides a unified framework for both the flat semi-convex and displacement convex cases. Additionally, we establish sharp chaos bounds for the quartic Curie-Weiss model in the sub-critical regime, demonstrating the generality of this method.

38 pages; accepted version

References in corpus (6)

• Transportation cost-information inequalities and applications to random dynamical systems and diffusions
• Hierarchies, entropy, and quantitative propagation of chaos for mean field diffusions
• A new approach to the mean-field limit of Vlasov-Fokker-Planck equations
• Uniform-in-time propagation of chaos for kinetic mean field Langevin dynamics
• Mean-field limit of non-exchangeable systems
• Higher-order propagation of chaos in $L^2$ for interacting diffusions