  We derive the linear acoustic and Stokes-Fourier equations as the limiting
dynamics of a system of N hard spheres of diameter $\epsilon$ in two space
dimensions, when N $\rightarrow$ $\infty$, $\epsilon$ $\rightarrow$ 0, N
$\epsilon$ = $\alpha$ $\rightarrow$ $\infty$, using the linearized Boltzmann
equation as an intermediate step. Our proof is based on Lanford's strategy
[18], and on the pruning procedure developed in [5] to improve the convergence
time to all kinetic times with a quantitative control which allows us to reach
also hydrodynamic time scales. The main novelty here is that uniform L 2 a
pri-ori estimates combined with a subtle symmetry argument provide a weak
version of chaos, in the form of a cumulant expansion describing the asymptotic
decorrelation between the particles. A refined geometric analysis of
recollisions is also required in order to discard the possibility of multiple
recollisions.
