  We consider the dynamics of a harmonic crystal in the half-space with zero
boundary condition. It is assumed that the initial date is a random function
with zero mean, finite mean energy density which also satisfies a mixing
condition of Rosenblatt or Ibragimov type. We study the distribution $\mu_t$ of
the solution at time $t\in\R$. The main result is the convergence of $\mu_t$ to
a Gaussian measure as $t\to\infty$ which is time stationary with a covariance
inherited from the initial (in general, non-Gaussian) measure.
