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June 2013 Examples of nonpolygonal limit shapes in i.i.d. first-passage percolation and infinite coexistence in spatial growth models
Michael Damron, Michael Hochman
Ann. Appl. Probab. 23(3): 1074-1085 (June 2013). DOI: 10.1214/12-AAP864

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.

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Michael Damron. Michael Hochman. "Examples of nonpolygonal limit shapes in i.i.d. first-passage percolation and infinite coexistence in spatial growth models." Ann. Appl. Probab. 23 (3) 1074 - 1085, June 2013. https://doi.org/10.1214/12-AAP864

Information

Published: June 2013
First available in Project Euclid: 7 March 2013

zbMATH: 1314.60154
MathSciNet: MR3076678
Digital Object Identifier: 10.1214/12-AAP864

Subjects:
Primary: 60K35
Secondary: 82B43

Keywords: extreme points , First-passage percolation , graph of infection , Limit shapes , Richardson’s growth model

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.23 • No. 3 • June 2013
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