Containing internal diffusion limited aggregation

Hugo Duminil-Copin (Université de Genève)
Cyrille Lucas (Université Paris 10)
Ariel Yadin (Ben Gurion University)
Amir Yehudayoff (Technion-IIT)


Internal Diffusion Limited Aggregation (IDLA) is a model that describes the growth of a random aggregate of particles from the inside out. Shellef proved that IDLA processes on supercritical percolation clusters of integer-lattices fill Euclidean balls, with high probability. In this article, we complete the picture and prove a limit-shape theorem for IDLA on such percolation clusters, by providing the corresponding upper bound.

The technique to prove upper bounds is new and robust: it only requires the existence of a ``good'' lower bound. Specifically, this way of proving upper bounds on IDLA clusters is more suitable for random environments than previous ways, since it does not harness harmonic measure estimates.

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Pages: 1-8

Publication Date: June 26, 2013

DOI: 10.1214/ECP.v18-2862


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