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Published online by Cambridge University Press: 14 August 2020
Internal diffusion-limited aggregation (IDLA) is a stochastic growth model on a graph G which describes the formation of a random set of vertices growing from the origin (some fixed vertex) of G. Particles start at the origin and perform simple random walks; each particle moves until it lands on a site which was not previously visited by other particles. This random set of occupied sites in G is called the IDLA cluster. In this paper we consider IDLA on Sierpinski gasket graphs, and show that the IDLA cluster fills balls (in the graphmetric) with probability 1.
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