  We consider a one-dimensional diffusion process with coefficients that are
periodic outside of a finite 'interface region'. The question investigated in
this article is the limiting long time / large scale behaviour of such a
process under diffusive rescaling. Our main result is that it converges weakly
to a rescaled version of skew Brownian motion, with parameters that can be
given explicitly in terms of the coefficients of the original diffusion.
  Our method of proof relies on the framework provided by Freidlin and Wentzell
for diffusion processes on a graph in order to identify the generator of the
limiting process. The graph in question consists of one vertex representing the
interface region and two infinite segments corresponding to the regions on
either side.
