  We derive an anomalous, sub-diffusive scaling limit for a one-dimensional
version of the Mott random walk. The limiting process can be viewed
heuristically as a one-dimensional diffusion with an absolutely continuous
speed measure and a discontinuous scale function, as given by a two-sided
stable subordinator. Corresponding to intervals of low conductance in the
discrete model, the discontinuities in the scale function act as barriers off
which the limiting process reflects for some time before crossing. We also
discuss how, by incorporating a Bouchaud trap model element into the setting,
it is possible to combine this 'blocking' mechanism with one of 'trapping'. Our
proof relies on a recently developed theory that relates the convergence of
processes to that of associated resistance metric measure spaces.
