  A coarse-grained stochastic hydrodynamical description of velocity and
concentration fluctuations in steadily sedimenting suspensions is constructed,
and analyzed using self-consistent and renormalization group methods. We find
that there exists a dynamical, non-equilibrium phase transition from an
"unscreened" phase in which we recover the Caflisch-Luke (R.E. Caflisch and
J.H.C. Luke, Phys. Fluids 28, 759 (1985)) divergence of the velocity variance
to a "screened" phase where the velocity fluctuations have a finite correlation
length growing as $\phi^{-1/3}$ where $\phi$ is the particle volume fraction,
in agreement with Segr\`e et. al. (Phys. Rev. Lett. 79, 2574 (1997)) and the
velocity variance is independent of system size. Detailed predictions are made
for the correlation function in both phases and at the transition.
