Diffusion in disordered media as a process with memory
  The problem of a random walk in a disordered media is mapped into a model of a random walk with memory. The latter model, as opposed to the former one, does not make reference to a particular realization of the disorder. The equivalence of the two models implies that the new model retrieves dynamically a realization of disorder; the only one which is consistent with its dynamics. In this new approach to the dynamics in disordered media, effects of memory, aging and the peculiar localization properties of the random walker, appear quite natural. 
Michele Vendruscolo and Matteo Marsili