We study the poor-biased model for money exchange introduced in Cao & Motsch ((2023) Kinet. Relat. Models 16(5), 764–794.): agents are being randomly picked at a rate proportional to their current wealth, and then the selected agent gives a dollar to another agent picked uniformly at random. Simulations of a stochastic system of finitely many agents as well as a rigorous analysis carried out in Cao & Motsch ((2023) Kinet. Relat. Models 16(5), 764–794.), Lanchier ((2017) J. Stat. Phys. 167(1), 160–172.) suggest that, when both the number of agents and time become large enough, the distribution of money among the agents converges to a Poisson distribution. In this manuscript, we establish a uniform-in-time propagation of chaos result as the number of agents goes to infinity, which justifies the validity of the mean-field deterministic infinite system of ordinary differential equations as an approximation of the underlying stochastic agent-based dynamics.

中文翻译：

---

美元交换经济物理模型的混沌均匀传播

我们研究了 Cao 和 Motsch ((2023) 中引入的货币兑换的贫偏模型基内特。相关。楷模16(5), 764–794.)：按照与当前财富成正比的比例随机挑选代理人，然后选定的代理人将一美元给予另一个随机挑选的代理人。有限多个智能体的随机系统的模拟以及 Cao 和 Motsch 中进行的严格分析 ((2023)基内特。相关。楷模16(5), 764–794.)，兰契尔 ((2017)J. 统计。物理。167(1), 160–172.)表明，当代理人的数量和时间都足够大时，代理人之间的货币分布收敛于泊松分布。在这份手稿中，我们建立了当智能体数量趋于无穷大时混沌结果的均匀时间传播，这证明了常微分方程的平均场确定性无限系统作为底层随机智能体的近似的有效性 -基于动力学。