The Annals of Probability

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

Nicolas Fournier and Stéphane Mischler

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Abstract

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.

Article information

Source
Ann. Probab., Volume 44, Number 1 (2016), 589-627.

Dates
Received: February 2013
Revised: May 2014
First available in Project Euclid: 2 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.aop/1454423051

Digital Object Identifier
doi:10.1214/14-AOP983

Mathematical Reviews number (MathSciNet)
MR3456347

Zentralblatt MATH identifier
1341.82060

Subjects
Primary: 80C40 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Kinetic theory stochastic particle systems propagation of chaos Wasserstein distance

Citation

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


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