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

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

2010-09-13

arxiv.org/abs/1009.2523v2

Mathematics

Probability

9 pages. Version 2: minor changes to presentation, corrected the statements of Marchand's and Hoffman's results, removed the b

Scientific paper

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 has extreme points which 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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