Examples of nonpolygonal limit shapes in i.i.d. first-passage percolation and infinite coexistence in spatial growth models

Michael Damron, Michael Hochman

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We construct an edge-weight distribution for i.i.d. first-passage percolation on Z2 whose limit shape is not a polygon and whose extreme points are arbitrarily dense in the boundary. Consequently, the associated Richardsontype growth model can support coexistence of a countably infinite number of distinct species, and the graph of infection has infinitely many ends.

Original languageAmerican English
Pages (from-to)1074-1085
Number of pages12
JournalAnnals of Applied Probability
Volume23
Issue number3
DOIs
StatePublished - Jun 2013
Externally publishedYes

Keywords

  • Extreme points
  • First-passage percolation
  • Graph of infection
  • Limit shapes
  • Richardson's growth model

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