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

Michael Damron; Michael Hochman

doi:10.1214/12-AAP864

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 journal › Article › peer-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 language	English
Pages (from-to)	1074-1085
Number of pages	12
Journal	Annals of Applied Probability
Volume	23
Issue number	3
DOIs	https://doi.org/10.1214/12-AAP864
State	Published - Jun 2013
Externally published	Yes

Keywords

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

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10.1214/12-AAP864

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AB - 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.

KW - Extreme points

KW - First-passage percolation

KW - Graph of infection

KW - Limit shapes

KW - Richardson's growth model

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

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Keywords

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