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Containing Internal Diffusion Limited Aggregation

Lucas, Cyrille
Yadin, Ariel
Yehudayoff, Amir
Published in Electronic Communications in Probability. 2013, vol. 18, no. 50, p. 1-8
Abstract 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.
arXiv: 1111.0486
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DUMINIL-COPIN, Hugo et al. Containing Internal Diffusion Limited Aggregation. In: Electronic Communications in Probability, 2013, vol. 18, n° 50, p. 1-8. doi: 10.1214/ECP.v18-2862 https://archive-ouverte.unige.ch/unige:30549

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Deposited on : 2013-10-21

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