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October 2019 Pathwise convergence of the hard spheres Kac process
Daniel Heydecker
Ann. Appl. Probab. 29(5): 3062-3127 (October 2019). DOI: 10.1214/19-AAP1475

Abstract

We derive two estimates for the deviation of the $N$-particle, hard-spheres Kac process from the corresponding Boltzmann equation, measured in expected Wasserstein distance. Particular care is paid to the long-time properties of our estimates, exploiting the stability properties of the limiting Boltzmann equation at the level of realisations of the interacting particle system. As a consequence, we obtain an estimate for the propagation of chaos, uniformly in time and with polynomial rates, as soon as the initial data has a $k$th moment, $k>2$. Our approach is similar to Kac’s proposal of relating the long-time behaviour of the particle system to that of the limit equation. Along the way, we prove a new estimate for the continuity of the Boltzmann flow measured in Wasserstein distance.

Citation

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Daniel Heydecker. "Pathwise convergence of the hard spheres Kac process." Ann. Appl. Probab. 29 (5) 3062 - 3127, October 2019. https://doi.org/10.1214/19-AAP1475

Information

Received: 1 January 2018; Revised: 1 August 2018; Published: October 2019
First available in Project Euclid: 18 October 2019

zbMATH: 07155067
MathSciNet: MR4019883
Digital Object Identifier: 10.1214/19-AAP1475

Subjects:
Primary: 60J25, 60K35
Secondary: 35Q20

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 5 • October 2019
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