Ordering in spatially-hetergeneous voter models

In the voter model, the state of a site is randomly copied from one of its neighbours. This results in an ordering process that is largely driven by fluctuations (as opposed to surface tension, as is the case in the Ising model). A remarkable observation, made in a number of recent papers in the physics literature (and not-so-recent papers in the mathematical biology literature), is that the stochastic equation of motion that is exact for the voter model on a fully-connected (mean-field) network also works pretty well on networks with non-trivial topology (albeit with a renormalised rate of ordering). I will explain some recent progress in my own understanding of when this 'mean-field approximation' is, in fact, not an approximation, and - if time permits - demonstrate its validity for a bunch of specific networks.