Abstract
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 language | English |
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Pages (from-to) | 517-549 |
Number of pages | 33 |
Journal | Annals of Applied Probability |
Volume | 27 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2017 |
Externally published | Yes |
Keywords
- Eden model
- First passage percolation
- Tree
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty