  We describe the diffusion and random velocities of solid particles due to
stochastic forcing by turbulent gas. We include the orbital dynamics of
Keplerian disks, both in-plane epicycles and vertical oscillations. We obtain a
new result for the diffusion of solids. The Schmidt number (ratio of gas to
particle diffusivity) is Sc = 1 + (Omega t_stop)^2, in terms of the particle
stopping time, t_stop, and the orbital frequency, Omega. The standard result,
Sc = 1 + t_stop/t_eddy, in terms of the eddy turnover time, t_eddy, is shown to
be incorrect. The main difference is that Sc rises quadratically, not linearly,
with stopping time. Consequently, particles larger than ~ 10 cm in
protoplanetary disks will suffer less radial diffusion and will settle closer
to the midplane. Such a layer of boulders would be more prone to gravitational
collapse. Our predictions of RMS speeds, vertical scale height and diffusion
coefficients will help interpret numerical simulations. We confirm previous
results for the vertical stirring of particles (scale heights and random
velocities), and add a correction for arbitrary ratios of eddy to orbital
times. The particle layer becomes thinner for t_eddy > 1/Omega, with the
strength of turbulent diffusion held fixed. We use two analytic techniques --
the Hinze-Tchen formalism and the Fokker-Planck equation with velocity
diffusion -- with identical results when the regimes of validity overlap. We
include simple physical arguments for the scaling of our results.
