We prove propagation of chaos at explicit polynomial rates in Wasserstein distance W2 for Kac’s N-particle system associated with the spatially homogeneous Boltzmann equation for Maxwell molecules. 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 W22.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics