  We consider a random walk on the support of a stationary simple point process
on $R^d$, $d\geq 2$ which satisfies a mixing condition w.r.t.the translations
or has a strictly positive density uniformly on large enough cubes. Furthermore
the point process is furnished with independent random bounded energy marks.
The transition rates of the random walk decay exponentially in the jump
distances and depend on the energies through a factor of the Boltzmann-type.
This is an effective model for the phonon-induced hopping of electrons in
disordered solids within the regime of strong Anderson localization. We show
that the rescaled random walk converges to a Brownian motion whose diffusion
coefficient is bounded below by Mott's law for the variable range hopping
conductivity at zero frequency. The proof of the lower bound involves estimates
for the supercritical regime of an associated site percolation problem.
