UNIFORM-IN-TIME PROPAGATION OF CHAOS FOR THE CUCKER–SMALE MODEL

Nicolai Jurek Gerber; Urbain Vaes

doi:10.3934/krm.2025021

UNIFORM-IN-TIME PROPAGATION OF CHAOS FOR THE CUCKER–SMALE MODEL

Nicolai Jurek Gerber
, Urbain Vaes

University of Ulm

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	56-79
Number of pages	24
Journal	Kinetic and Related Models
Volume	20
DOIs	https://doi.org/10.3934/krm.2025021
Publication status	Published - 1 Apr 2026

Keywords

Cucker–Smale model
interacting particle system
uniform-in-time mean-field limits
uniform-in-time propagation of chaos

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10.3934/krm.2025021

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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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AB - 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.

KW - Cucker–Smale model

KW - interacting particle system

KW - uniform-in-time mean-field limits

KW - uniform-in-time propagation of chaos

UR - https://www.scopus.com/pages/publications/105027954669

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JO - Kinetic and Related Models

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ER -

UNIFORM-IN-TIME PROPAGATION OF CHAOS FOR THE CUCKER–SMALE MODEL

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