QUANTITATIVE PROPAGATION OF CHAOS FOR GENERALIZED KAC PARTICLE SYSTEMS

• 成果类型: Article
• 署名作者: Cortez, Roberto; Fontbona, Joaquin
• 署名单位: Universidad de Chile; Universidad de Chile
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1107
• 发表日期: 2016
• 页码: 892-916
• 关键词: equation; models

摘要

We study a class of one-dimensional particle systems with true (Bird type) binary interactions, which includes Kac's model of the Boltzmann equation and nonlinear equations for the evolution of wealth distribution arising in kinetic economic models. We obtain explicit rates of convergence for the Wasserstein distance between the law of the particles and their limiting law, which are linear in time and depend in a mild polynomial manner on the number of particles. The proof is based on a novel coupling between the particle system and a suitable system of nonindependent nonlinear processes, as well as on recent sharp estimates for empirical measures.