Rate of convergence of the Nanbu particle system for hard potentials and Maxwell molecules
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
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1302.5810v2
Journal nameAnnals of Probability
Institute of Mathematical Statistics
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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 / KeywordsKinetic theory; Propagation of Chaos; Stochastic particle systems; Wasserstein distance
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