Kac's chaos and Kac's program
St\'ephane Mischler (CEREMADE)
TL;DR
This paper reviews key results on the propagation of chaos in the Boltzmann-Kac system, addressing questions posed by Kac, and discusses recent related findings by various researchers.
Contribution
It provides a comprehensive overview of quantitative and qualitative propagation of chaos results for the Boltzmann-Kac system, including collaborative work and recent developments.
Findings
Quantitative propagation of chaos results
Qualitative propagation of chaos results
Connections to Kac's questions and program
Abstract
In this note I present the main results about the quantitative and qualitative propagation of chaos for the Boltzmann-Kac system obtained in collaboration with C. Mouhot in \cite{MMinvent} which gives a possible answer to some questions formulated by Kac in \cite{Kac1956}. We also present some related recent results about Kac's chaos and Kac's program obtained in \cite{MMWchaos,HaurayMischler,KleberSphere} by K. Carrapatoso, M. Hauray, C. Mouhot, B. Wennberg and myself.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Gas Dynamics and Kinetic Theory · Advanced Thermodynamics and Statistical Mechanics