Uniform propagation of chaos for a dollar exchange model

Co-author of the paper ‘Uniform propagation of chaos for a dollar exchange model’, Fei Cao, introduces the research theory influencing the article from the peer reviewed academic research paper is published by Cambridge University Press, in the journal European Journal of Applied Mathematics (April 2024). This research paper, written by Fei Cao and Roberto Cortez, is part of: Markov processes, mathematical economics, and time-dependent statistical mechanics (dynamic and nonequilibrium).
Paper abstract: ‘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.’ - European Journal of Applied Mathematics, Cambridge Core.
TOPICS:
Econophysics, agent-based model, uniform propagation of chaos, coupling, Wasserstein distance
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