  From the exact single step evolution equation of the two-point correlation
function of a particle distribution subjected to a stochastic displacement
field $\bu(\bx)$, we derive different dynamical regimes when $\bu(\bx)$ is
iterated to build a velocity field. First we show that spatially uncorrelated
fields $\bu(\bx)$ lead to both standard and anomalous diffusion equation. When
the field $\bu(\bx)$ is spatially correlated each particle performs a simple
free Brownian motion, but the trajectories of different particles result to be
mutually correlated. The two-point statistical properties of the field
$\bu(\bx)$ induce two-point spatial correlations in the particle distribution
satisfying a simple but non-trivial diffusion-like equation. These
displacement-displacement correlations lead the system to three possible
regimes: coalescence, simple clustering and a combination of the two. The
existence of these different regimes, in the one-dimensional system, is shown
through computer simulations and a simple theoretical argument.
