Quantitative concentration inequalities for empirical measures on non-compact spaces

• 成果类型: Article
• 署名作者: Bolley, Francois; Guillin, Arnaud; Villani, Cedric
• 署名单位: Ecole Normale Superieure de Lyon (ENS de LYON); Universite PSL; Universite Paris-Dauphine
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-006-0004-7
• 发表日期: 2007
• 页码: 541-593
• 关键词: self-stabilizing processes; granular media; CONVERGENCE; EXISTENCE; EQUATIONS

摘要

We establish quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances. As an application, we provide some error bounds for particle simulations in a model mean field problem. The tools include coupling arguments, as well as regularity and moment estimates for solutions of certain diffusive partial differential equations.