Uniform Propagation of Chaos for the Thermostated Kac Model
Uniform Propagation of Chaos for the Thermostated Kac Model
复制标题
恒温 Kac 模型的混沌均匀传播
DOI：
10.1007/s10955-021-02763-9
复制
发表时间：
2020
影响因子：
1.6
通讯作者：
H. Tossounian
中科院分区：
文献类型：
--
作者：
R. Cortez;H. Tossounian
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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N^{-1/3}$$\end{document} 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.
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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N^{-1/3}$$\end{document} 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.