  A linear Boltzmann equation is derived in the Boltzmann-Grad scaling for the
deterministic dynamics of many interacting particles with random initial data.
We study a Rayleigh gas where a tagged particle is undergoing hard-sphere
collisions with background particles, which do not interact among each other.
In the Boltzmann-Grad scaling, we derive the validity of a linear Boltzmann
equation for arbitrary long times under moderate assumptions on higher moments
of the initial distributions of the tagged particle and the possibly
non-equilibrium distribution of the background. The convergence of the empiric
dynamics to the Boltzmann dynamics is shown using Kolmogorov equations for
associated probability measures on collision histories.
