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

Abstract

We construct an edge-weight distribution for i.i.d. first-passage percolation on ${\mathbb{Z}}^2$ whose limit shape is not a polygon and whose extreme points are arbitrarily dense in the boundary. Consequently, the associated Richardson-type growth model can support coexistence of a countably infinite number of distinct species, and the graph of infection has infinitely many ends.

Published in at http://dx.doi.org/10.1214/12-AAP864 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• Shape of territories in some competing growth models
• Shape curvatures and transversal fluctuations in the first passage percolation model

Cited by in corpus (5)

• Limiting geodesics for first-passage percolation on subsets of ${\mathbb{Z}}^2$
• Differentiability at the edge of the percolation cone and related results in first-passage percolation
• Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman
• First contact percolation
• Existence and coalescence of directed infinite geodesics in the percolation cone for Durrett-Liggett class of measures