Scaling limits for diffusion on a comb structure

I will describe some diffusion processes on periodic comb-like structures and their scaling limit, which is a Brownian motion subordinated to an independent sticky Brownian motion. This limit process may exhibit anomalous diffusion. This work is motivated in part by studies of diffusion and homogenization in media which are not uniformly elliptic. I will describe the scaling limit from the point of view of SDEs and from the point of view of Ito excursion theory. The latter approach also makes connections with recent work on trapped random walks. This is joint work with Sam Cohn, Gautam Iyer, and Bob Pego from Carnegie Mellon University.