  In this work we study the diffusion of non-interacting overdamped particles,
moving on unbiased disordered correlated potentials, subjected to Gaussian
white noise. We obtain an exact expression for the diffusion coefficient which
allows us to prove that the unbiased diffusion of overdamped particles on a
random polymer does not depend on the correlations of the disordered
potentials. This universal behavior of the unbiased diffusivity is a direct
consequence of the validity of the Einstein relation and the decay of
correlations of the random polymer. We test the independence on correlations of
the diffusion coefficient for correlated polymers produced by two different
stochastic processes, a one-step Markov chain and the expansion-modification
system. Within the accuracy of our simulations, we found that the numerically
obtained diffusion coefficient for these systems agree with the analytically
calculated ones, confirming our predictions.
