  The physical properties of granular materials have been extensively studied
in recent years. So far, however, there exists no theoretical framework which
can explain the observations in a unified manner beyond the phenomenological
jamming diagram [1]. This work focuses on the case of static granular matter,
where we have constructed a statistical ensemble [2] which mirrors equilibrium
statistical mechanics. This ensemble, which is based on the conservation
properties of the stress tensor, is distinct from the original Edwards ensemble
and applies to packings of deformable grains. We combine it with a field
theoretical analysis of the packings, where the field is the Airy stress
function derived from the force and torque balance conditions. In this
framework, Point J characterized by a diverging stiffness of the pressure
fluctuations. Separately, we present a phenomenological mean-field theory of
the jamming transition, which incorporates the mean contact number as a
variable. We link both approaches in the context of the marginal rigidity
picture proposed by [3, 4].
