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

Fournier, Nicolas ^[1] ; Mischler, Stéphane ^[2]
1. [1] Pierre and Marie Curie University
  
  Pierre and Marie Curie University
  
  París, Francia
2. [2] Paris Dauphine University
  
  Paris Dauphine University
  
  París, Francia
Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 1, 2016, págs. 589-627
Idioma: inglés
DOI: 10.1214/14-AOP983
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Resumen
- 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.