  We study the diffusion of an ensemble of overdamped particles sliding over a
tilted random poten- tial (produced by the interaction of a particle with a
random polymer) with long-range correlations. We found that the diffusion
properties of such a system are closely related to the correlation function of
the corresponding potential. We model the substrate as a symbolic trajectory of
a shift space which enables us to obtain a general formula for the diffusion
coefficient when normal diffusion occurs. The total time that the particle
takes to travel through n monomers can be seen as an ergodic sum to which we
can apply the central limit theorem. The latter can be implemented if the
correlations decay fast enough in order for the central limit theorem to be
valid. On the other hand, we presume that when the central limit theorem breaks
down the system give rise to anomalous diffusion. We give two examples
exhibiting a transition from normal to anomalous diffusion due to this
mechanism. We also give analytical expressions for the diffusion exponents in
both cases by assuming convergence to a stable law. Finally we test our
predictions by means of numerical simulations.
