  We consider the Dirac equation in $\R^3$ with a potential, and study the
distribution $\mu_t$ of the random solution at time $t\in\R$. The initial
measure $\mu_0$ has zero mean, a translation-invariant covariance, and a finite
mean charge density. We also assume that $\mu_0$ satisfies a mixing condition
of Rosenblatt- or Ibragimov-Linnik-type. The main result is the long time
convergence of projection of $\mu_t$ onto the continuous spectral space. The
limiting measure is Gaussian.
