PROPAGATION OF CHAOS FOR TOPOLOGICAL INTERACTIONS

• 成果类型: Article
• 署名作者: Degond, P.; Pulvirenti, M.
• 署名单位: Imperial College London; University of L'Aquila
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1469
• 发表日期: 2019
• 页码: 2594-2612
• 关键词: boltzmann-grad limit; mean-field limit; global validity; rare-gas; EQUATIONS; systems; CONVERGENCE; particles; flocking; forces

摘要

We consider a N-particle model describing an alignment mechanism due to a topological interaction among the agents. We show that the kinetic equation, expected to hold in the mean-field limit N -> infinity, as following from the previous analysis in (J. Stat. Phys. 163 (2016) 41-60) can be rigorously derived. This means that the statistical independence (propagation of chaos) is indeed recovered in the limit, provided it is assumed at time zero.