  We consider the trajectory of a tracer that is the solution of an ordinary
differential equation $\dot\bbX(t)=\bbV(t, \bbX(t)),\ X(0)=0$, with the right
hand side, that is a stationary, zero-mean, Gaussian vector field with
incompressible realizations. It is known, see [K-F;C-X;K-L-O], that
$\bbX(t)/\sqrt{t}$ converges in law, as $t\to+\infty$, to a normal, zero mean
vector, provided that the field $V(t,x)$ is Markovian and has the spectral gap
property. We wish to extend this result to the case when the field is not
Markovian and its covariance matrix is given by a completely monotone Bernstein
function.
