  We study the linear response in different models of driven granular gases. In
some situations, even if the the velocity statistics can be strongly
non-Gaussian, we do not observe appreciable violations of the Einstein formula
for diffusion versus mobility. The situation changes when strong correlations
between velocities and density are present: in this case, although a form of
fluctuation-dissipation relation holds, the differential velocity response of a
particle and its velocity self-correlation are no more proportional. This
happens at high densities and strong inelasticities, but still in the
fluid-like (and ergodic) regime.
