Containing internal diffusion limited aggregation

Hugo Duminil-Copin, Cyrille Lucas, Ariel Yadin, Amir Yehudayoff

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number50
JournalElectronic Communications in Probability
StatePublished - 9 Jul 2013


  • Idla
  • Percolation
  • Random walk

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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