  The initial-boundary value problem for an infinite one-dimensional chain of
harmonic oscillators on the half-line is considered. The large time asymptotic
behavior of solutions is studied. The initial data of the system are supposed
to be a random function which has some mixing properties. We study the
distribution $\mu_t$ of the random solution at time moments $t\in\mathbb{R}$.
The main result is the convergence of $\mu_t$ to a Gaussian probability measure
as $t\to\infty$. We find stationary states in which there is a non-zero energy
current at origin.
