Kac's chaos and Kac's program
Résumé
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.
Mots clés
Kac's program
Kac's chaos
kinetic theory
master equation
mean-field limit
jump process
collision process
Boltzmann equation
Maxwell molecules
non cutoff
hard spheres
Monge-Kantorovich-Wasserstein distance
entropy chaos
Fisher information chaos
CLT with optimal rate
quantitative chaos
qualitative chaos
uniform in time.
uniform in time
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