Thursday, March 14, 2013

1009.2523 (Michael Damron et al.)

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

Michael Damron, Michael Hochman
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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