Stationary Probability Distribution in Granular Media

We discuss recent developments in the formulation of a Statistical Mechanics approach to non thermal systems, such as granular media. We review a few important numerical results on the assessment of Edwards' theory and, in particular, we apply these ideas to study a mean field model of a hard sphere binary mixture under gravity, which can be fully analytically investigated. As a consequence, we derive the rich phase diagram and predict the features of segregation patterns of the mixture.