The stochastic growth model Internal Diffusion Limited Aggregation was defined in 1991 by Diaconis and Fulton. Several shape results are known when the underlying state space is the d-dimensional lattice, or a discrete group with exponential growth. We prove an extension of the shape result of Blachere and Brofferio for Internal Diffusion Limited Aggregation on a wide class of Markov chains on non-amenable graphs.
"Internal Diffusion-Limited Aggregation on non-amenable graphs." Electron. Commun. Probab. 13 272 - 279, 2008. https://doi.org/10.1214/ECP.v13-1374