Stationary Eden model on Cayley graphs

Tonći Antunović, Eviatar B. Procaccia

Research output: Contribution to journalArticlepeer-review


We consider two stationary versions of the Eden model, on the upper half planar lattice, resulting in an infinite forest covering the half plane. Under weak assumptions on the weight distribution and by relying on ergodic theorems, we prove that almost surely all trees are finite. Using the mass transport principle, we generalize the result to Eden model in graphs of the form G x double-struck Z+, where G is a Cayley graph. This generalizes certain known results on the two-type Richardson model, in particular of Deijfen and Häggström in 2007.

Original languageEnglish
Pages (from-to)517-549
Number of pages33
JournalAnnals of Applied Probability
Issue number1
StatePublished - Feb 2017
Externally publishedYes


  • Eden model
  • First passage percolation
  • Tree

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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