PROPAGATION OF CHAOS FOR TOPOLOGICAL INTERACTIONS

被引：11
|
作者：
Degond, P. [1 ]
Pulvirenti, M. [2 ]
机构：
[1] Imperial Coll London, Dept Math, London SW7 2AZ, England
[2] Univ Aquila, Int Res Ctr Math & Mech Complex Syst MEMOCS, I-67100 Laquila, Italy
来源：
ANNALS OF APPLIED PROBABILITY | 2019年 / 29卷 / 04期
基金：
英国工程与自然科学研究理事会; 美国国家科学基金会;
关键词：
Rank-based interactions; Boltzmann equation; BOLTZMANN-GRAD LIMIT; MEAN-FIELD LIMIT; GLOBAL VALIDITY; RARE-GAS; EQUATIONS; SYSTEMS; CONVERGENCE; PARTICLES; FLOCKING; FORCES;
D O I：
10.1214/19-AAP1469
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
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.
引用
收藏
页码：2594 / 2612
页数：19
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