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

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Date
2016
Publisher city
Paris
Link to item file
https://arxiv.org/abs/1302.5810v2
Dewey
Probabilités et mathématiques appliquées
Sujet
Kinetic theory; Propagation of Chaos; Stochastic particle systems; Wasserstein distance
Journal issue
Annals of Probability
Volume
44
Number
1
Publication date
2016
Article pages
589-627
Publisher
Institute of Mathematical Statistics
DOI
http://dx.doi.org/10.1214/14-AOP983
URI
https://basepub.dauphine.fr/handle/123456789/11071
Collections
  • CEREMADE : Publications
Metadata
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Author
Mischler, Stéphane
Fournier, Nicolas
Type
Article accepté pour publication ou publié
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.

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