  We study statistical properties of vibrated granular monolayers using
molecular dynamics simulations. We show that at high excitation strengths, the
system is in a gas state, particle motion is isotropic, and the velocity
distributions are Gaussian. As the vibration strength is lowered the system's
dimensionality is reduced from three to two. Below a critical excitation
strength, a gas-cluster phase occurs, and the velocity distribution becomes
bimodal. In this phase, the system consists of clusters of immobile particles
arranged in close-packed hexagonal arrays, and gas particles whose energy
equals the first excited state of an isolated particle on a vibrated plate.
