The nonequilibrium steady state of a granular fluid, driven by a random ext
ernal force, is demonstrated to exhibit long-range correlations, which beha
ve as similar to 1/r in three and similar to ln(L/r) in two dimensions. We
calculate the corresponding structure factors over the whole range of wave
numbers, and find good agreement with two-dimensional molecular dynamics si
mulations. It is also shown by means of a mode coupling calculation, how th
e mean field values for the steady-state temperature and collision frequenc
y, as obtained from the Enskog-Boltzmann equation, are renormalized by long
wavelength hydrodynamic fluctuations.