  We analyse the motion of a system of particles subjected a random force
fluctuating in both space and time, and experiencing viscous damping. When the
damping exceeds a certain threshold, the system undergoes a phase transition:
the particle trajectories coalesce. We analyse this transition by mapping it to
a Kramers problem which we solve exactly. In the limit of weak random force we
characterise the dynamics by computing the rate at which caustics are crossed,
and the statistics of the particle density in the coalescing phase. Last but
not least we describe possible realisations of the effect, ranging from
trajectories of raindrops on glass surfaces to animal migration patterns.
