  We investigate a phase separation instability that occurs in a system of
nearly elastically colliding hard spheres driven by a thermal wall. If the
aspect ratio of the confining box exceeds a threshold value, granular
hydrostatics predict phase separation: the formation of a high-density region
coexisting with a low-density region along the wall that is opposite to the
thermal wall. Event-driven molecular dynamic simulations confirm this
prediction. The theoretical bifurcation curve agrees with the simulations
quantitatively well below and well above the threshold. However, in a wide
region of aspect ratios around the threshold, the system is dominated by
fluctuations, and the hydrostatic theory breaks down. Two possible scenarios of
the origin of the giant fluctuations are discussed.
