Size of chaos for Gibbs measures of mean field interacting diffusions

• 成果类型: Article; Early Access
• 署名作者: Ren, Zhenjie; Wang, Songbo
• 署名单位: Universite Cote d'Azur
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-025-01435-z
• 发表日期: 2025
• 关键词: logarithmic sobolev inequalities; transportation cost; propagation; systems

摘要

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.