  A nonlinear two-fluid stochastic hydrodynamical description of velocity and
concentration fluctuations in sedimenting suspensions is constructed, and
analyzed using self-consistent (SC) and renormalization group (RG) methods. The
advection of particles by velocity fluctuations is shown to be ``relevant'' in
all dimensions $d < 6$ . Both RG and SC analyses predict a strong reduction in
the dependence of velocity fluctuations on system-size $L$ relative to the
$L^{1/2}$ obtained in the linearized theory of Caflisch and Luke [Phys. Fluids
{\bf 28}, 785 (1985)]. This is an important step towards resolving a ten-year
old puzzle in the field.
