On the dynamics of dilute gases

The evolution of a gas can be described by different mathematical models depending on the scale of observation. A natural question, raised by Hilbert in his sixth problem, is whether these models provide mutually consistent predictions. In particular, for rarefied gases, it is expected that the equations of the kinetic theory of gases can be obtained from molecular dynamics governed by the fundamental principles of mechanics. In the case of hard sphere gases, Lanford [16] has shown that the Boltzmann equation does indeed appear as a law of large numbers in the low density limit, at least for very short times. The aim of this paper is to present recent advances in the understanding of this limiting process.