The Annals of Probability
- Ann. Probab.
- Volume 44, Number 1 (2016), 589-627.
Rate of convergence of the Nanbu particle system for hard potentials and Maxwell molecules
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.
Ann. Probab., Volume 44, Number 1 (2016), 589-627.
Received: February 2013
Revised: May 2014
First available in Project Euclid: 2 February 2016
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Fournier, Nicolas; Mischler, Stéphane. Rate of convergence of the Nanbu particle system for hard potentials and Maxwell molecules. Ann. Probab. 44 (2016), no. 1, 589--627. doi:10.1214/14-AOP983. https://projecteuclid.org/euclid.aop/1454423051