  The evolution of a gas can be described by different models depending on the
observation scale. A natural question, raised by Hilbert in his sixth problem,
is whether these models provide consistent predictions. In particular, for
rarefied gases, it is expected that continuum laws of kinetic theory can be
obtained directly from molecular dynamics governed by the fundamental
principles of mechanics. In the case of hard sphere gases, Lanford showed that
the Boltzmann equation emerges as the law of large numbers in the low density
limit, at least for very short times. The goal of this survey is to present
recent progress in the understanding of this limiting process, providing a
complete statistical description.
