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January 2016 Rate of convergence of the Nanbu particle system for hard potentials and Maxwell molecules
Nicolas Fournier, Stéphane Mischler
Ann. Probab. 44(1): 589-627 (January 2016). DOI: 10.1214/14-AOP983


We consider the (numerically motivated) Nanbu stochastic particle system associated to the spatially homogeneous Boltzmann equation for true hard potentials and Maxwell molecules. 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 to the Boltzmann equation. The rate we obtain is almost optimal as a function of the number of particles but is not uniform in time.


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Nicolas Fournier. Stéphane Mischler. "Rate of convergence of the Nanbu particle system for hard potentials and Maxwell molecules." Ann. Probab. 44 (1) 589 - 627, January 2016.


Received: 1 February 2013; Revised: 1 May 2014; Published: January 2016
First available in Project Euclid: 2 February 2016

zbMATH: 1341.82060
MathSciNet: MR3456347
Digital Object Identifier: 10.1214/14-AOP983

Primary: 60K35 , 80C40

Keywords: Kinetic theory , propagation of chaos , Stochastic particle systems , Wasserstein distance

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.44 • No. 1 • January 2016
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