Abstract

I will discuss various ways in which subdiffusive behaviour arises in random walk models in one dimension, including continuous time random walks, the Bouchaud trap model, the random conductance model and Mott variable range hopping. In particular, I will describe how subordinators can appear as scaling limits of certain time-change functionals, invariant measures, or the effective resistance of the associated electrical networks (which roughly plays the role of the scale function), and what this means for the scaling limit of the random walk. Much of the talk will be a review, but the part on Mott variable range hopping stems from a recent joint work with Ryoki Fukushima (University of Tsukuba) and Stefan Junk (Tohoku University).