  We consider lattice dynamics with a small stochastic perturbation of order
&#949; and prove that for a space-time scale of order \varepsilon\^-1 the local
spectral density (Wigner function) evolves according to a linear transport
equation describing inelastic collisions. For an energy and momentum conserving
chain the transport equation predicts a slow decay, as 1/\sqrt{t}, for the
energy current correlation in equilibrium. This is in agreement with previous
studies using a different method.
