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

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.

References in corpus (13)

• The Ensemble Kalman Filter for Inverse Problems
• A new model for self-organized dynamics and its flocking behavior
• A consensus-based model for global optimization and its mean-field limit
• Propagation of chaos: a review of models, methods and applications. II. Applications
• Hierarchies, entropy, and quantitative propagation of chaos for mean field diffusions
• Ensemble Kalman Inversion: mean-field limit and convergence analysis
• On Mean Field Limits for Dynamical Systems
• Ensemble Kalman Sampler: mean-field limit and convergence analysis
• Uniform long-time and propagation of chaos estimates for mean field kinetic particles in non-convex landscapes
• On the mean-field limit for the consensus-based optimization
• Consensus-Based Optimization Methods Converge Globally
• Heterogeneous gradient flows in the topology of fibered optimal transport
• Mean-field limits for Consensus-Based Optimization and Sampling