Translator Disclaimer
April 2022 A coupling approach for the convergence to equilibrium for a collisionless gas
Armand Bernou, Nicolas Fournier
Author Affiliations +
Ann. Appl. Probab. 32(2): 764-811 (April 2022). DOI: 10.1214/21-AAP1696

Abstract

We use a probabilistic approach to study the rate of convergence to equilibrium for a collisionless (Knudsen) gas in dimension equal to or larger than 2. The use of a coupling between two stochastic processes allows us to extend and refine, in total variation distance, the polynomial rate of convergence given in (Kinet. Relat. Models 4 (2011) 87–107) and (Comm. Math. Phys. 318 (2013) 375–409). This is, to our knowledge, the first quantitative result in collisionless kinetic theory in dimension equal to or larger than 2 that does not require any symmetry of the domain, nor a monokinetic regime. Our study is also more general in terms of reflection at the boundary: we allow for rather general diffusive reflections and for a specular reflection component.

Funding Statement

A.B. gratefully acknowledges support by grants from Région Ile-de-France.

Acknowledgments

The authors would like to thank the anonymous referee for their careful reading and useful comments.

Citation

Download Citation

Armand Bernou. Nicolas Fournier. "A coupling approach for the convergence to equilibrium for a collisionless gas." Ann. Appl. Probab. 32 (2) 764 - 811, April 2022. https://doi.org/10.1214/21-AAP1696

Information

Received: 1 October 2019; Revised: 1 October 2020; Published: April 2022
First available in Project Euclid: 28 April 2022

Digital Object Identifier: 10.1214/21-AAP1696

Subjects:
Primary: 60J25 , 82C40

Keywords: collisionless gas , coupling , Long-time behaviour , Markov process , Stochastic billiards , subexponential convergence to equilibrium

Rights: Copyright © 2022 Institute of Mathematical Statistics

JOURNAL ARTICLE
48 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.32 • No. 2 • April 2022
Back to Top