  The paper considers the wave equation, with constant or variable coefficients
in $\R^n$, with odd $n\geq 3$. We study the asymptotics of the distribution
$\mu_t$ of the random solution at time $t\in\R$ as $t\to\infty$. It is assumed
that the initial measure $\mu_0$ has zero mean, translation-invariant
covariance matrices, and finite expected energy density. We also assume that
$\mu_0$ satisfies a Rosenblatt- or Ibragimov-Linnik-type space mixing
condition. The main result is the convergence of $\mu_t$ to a Gaussian measure
$\mu_\infty$ as $t\to\infty$, which gives a Central Limit Theorem (CLT) for the
wave equation. The proof for the case of constant coefficients is based on an
analysis of long-time asymptotics of the solution in the Fourier representation
and Bernstein's `room-corridor' argument. The case of variable coefficients is
treated by using a version of the scattering theory for infinite energy
solutions, based on Vainberg's results on local energy decay.
