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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