The mixing boundary-value problem for infinite one-dimensional chain of harmonic oscillators on the half-line is considered. The large time asymptotic behavior of solutions is obtained. 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 $t\to\infty$. The mixing properties of the limit measures are studied.
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