Kac's chaos and Kac's program

Stéphane Mischler (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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

Domaines: Equations aux dérivées partielles [math.AP]

Stéphane Mischler. Kac's chaos and Kac's program. 2013. ⟨hal-00911426v2⟩