  We consider the Hamiltonian system consisting of a Klein-Gordon vector field
and a particle in $\R^3$. The initial date of the system is a random function
with a finite mean density of energy which also satisfies a Rosenblatt- or
Ibragimov-type mixing condition. Moreover, initial correlation functions are
translation-invariant. 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 $t\to\infty$, where $\mu_\infty$ is translation-invariant.
