  We investigate dynamically and statistically diffusive motion in a
Klein-Gordon particle chain in the presence of disorder. In particular, we
examine a low energy (subdiffusive) and a higher energy (self-trapping) case
and verify that subdiffusive spreading is always observed. We then carry out a
statistical analysis of the motion in both cases in the sense of the Central
Limit Theorem and present evidence of different chaos behaviors, for various
groups of particles. Integrating the equations of motion for times as long as
$10^9$, our probability distribution functions always tend to Gaussians and
show that the dynamics does not relax onto a quasi-periodic KAM torus and that
diffusion continues to spread chaotically for arbitrarily long times.
