Scaling limits in Kinetic theory
Summer School - Lyon - 2019

Minicourse by Freddy Bouchet (ENS de Lyon)

Kinetic theory and large deviation theory: from interacting particles to geophysical fluid dynamics and atmosphere jets

Most kinetic equations can be interpreted as laws of large numbers for the evolution of the empirical density. We will study the probability of departure from this law of large numbers, using large deviation theory. From this point of view, we will describe classical and more original kinetic equations: the Boltzmann equation, the Vlasov-McKean equation, and the effective description of large scale turbulent flows. We will establish the relation between the mathematical structure of the path probability large deviations and fundamental physical properties: entropy production and gradient structures. We will also stress the importance of large deviations for applications, for instance for abrupt climate changes of Jupiter's troposphere jets.