Rate of convergence of the Nanbu particle system for hard potentials

Nicolas Fournier (1) , Stéphane Mischler (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Mots clés: Kinetic theory; Stochastic particle systems; Propagation of Chaos; Wasserstein distance

Domaines: Equations aux dérivées partielles [math.AP]

Nicolas Fournier, Stéphane Mischler. Rate of convergence of the Nanbu particle system for hard potentials. Annals of Probability, 2016, 44 (1), pp.589-627. ⟨hal-00793662v2⟩