  We investigate the properties of a model of granular matter consisting of $N$
Brownian particles on a line subject to inelastic mutual collisions. This model
displays a genuine thermodynamic limit for the mean values of the energy and
the energy dissipation. When the typical relaxation time $\tau$ associated with
the Brownian process is small compared with the mean collision time $\tau_c$
the spatial density is nearly homogeneous and the velocity probability
distribution is gaussian. In the opposite limit $\tau \gg \tau_c$ one has
strong spatial clustering, with a fractal distribution of particles, and the
velocity probability distribution strongly deviates from the gaussian one.
