Uniform Propagation of Chaos for the Thermostated Kac Model

Roberto Cortez, Hagop Tossounian

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We consider Kac’s 1D N-particle system coupled to an ideal thermostat at a fixed temperature, introduced by Bonetto, Loss, and Vaidyanathan in 2014. We obtain a propagation of chaos result for this system, with an explicit and uniform-in-time rate of order N- 1 / 3 in terms of the 2-Wasserstein metric squared. We also show well-posedness and equilibration for the limit kinetic equation in the space of probability measures. The proofs use a coupling argument previously introduced by Cortez and Fontbona in 2016.

Original languageEnglish
Article number28
JournalJournal of Statistical Physics
Volume183
Issue number2
DOIs
Publication statusPublished - May 2021

Keywords

  • Coupling methods
  • Kac model
  • Kinetic theory of gases
  • Propagation of chaos
  • Thermostated Kac model

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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