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arXiv · 2501.15517

Uniform-in-time propagation of chaos for the Cucker--Smale model

Nicolai Jurek Gerber·Urbain Vaes
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Abstract

This paper presents an elementary proof of quantitative uniform-in-time propagation of chaos for the Cucker--Smale model under sufficiently strong interaction. The idea is to combine existing finite-time propagation of chaos estimates with existing uniform-in-time stability estimates for the interacting particle system, in order to obtain a uniform-in-time propagation of chaos estimate with an explicit rate of convergence in the number of particles. This is achieved via a method that is similar in spirit to the classical 'stability + consistency implies convergence' approach in numerical analysis.

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Nicolai Jurek Gerber, Urbain Vaes. 2025-01-26. Uniform-in-time propagation of chaos for the Cucker--Smale model. https://doi.org/10.3934/krm.2025021

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