Quantitative uniform propagation of chaos for Maxwell molecules

TL;DR

This paper establishes explicit polynomial convergence rates in Wasserstein distance for the propagation of chaos in Maxwell molecules' particle systems, using novel probabilistic coupling methods and stabilization results.

Contribution

It introduces new probabilistic coupling techniques to quantify uniform-in-time propagation of chaos for Maxwell molecules' systems with explicit rates.

Findings

Proves propagation of chaos with polynomial rates in Wasserstein distance.

Achieves uniform-in-time estimates of order almost N^{-1/3}.

Applies to Maxwell molecules with and without cutoff.

Abstract

We prove propagation of chaos at explicit polynomial rates in Wasserstein distance W_2 for Kac's N-particle system associated with the spatially homogeneous Boltzmann equation for Maxwell molecules, with and without cutoff. Our approach is mainly based on novel probabilistic coupling techniques. Combining them with recent stabilization results for the particle system we obtain, under suitable moments assumptions on the initial distribution, a uniform-in-time estimate of order almost N^{-1/3} for W_2^2.