Rate of convergence of the Nanbu particle system for hard potentials and Maxwell molecules

Mischler, Stéphane; Fournier, Nicolas

Mischler, Stéphane; Fournier, Nicolas (2016), Rate of convergence of the Nanbu particle system for hard potentials and Maxwell molecules, Annals of Probability, 44, 1, p. 589-627. 10.1214/14-AOP983

Type

Article accepté pour publication ou publié

External document link

https://arxiv.org/abs/1302.5810v2

Date

2016

Journal name

Annals of Probability

Volume

Number

Publisher

Institute of Mathematical Statistics

Published in

Paris

Pages

589-627

Abstract (EN)

We consider the (numerically motivated) Nanbu stochastic particle system associated to the spatially homogeneous Boltzmann equation for true hard potentials. We establish a rate of propagation of chaos of the particle system to the unique solution of the Boltzmann equation. More precisely, we estimate the expectation of the squared Wasserstein distance with quadratic cost between the empirical measure of the particle system and the solution. The rate we obtain is almost optimal as a function of the number of particles but is not uniform in time.

Subjects / Keywords

Kinetic theory; Propagation of Chaos; Stochastic particle systems; Wasserstein distance