Examples of nonpolygonal limit shapes in i.i.d. first-passage percolation and infinite coexistence in spatial growth models
Examples of nonpolygonal limit shapes in i.i.d. first-passage percolation and infinite coexistence in spatial growth models
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i.i.d. 中非多边形极限形状的示例
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
M. Hochman
中科院分区：
文献类型：
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作者：
M. Damron;M. Hochman
我们构建独立同分布的边权重分布。 $mathbb{Z}^2$ 上的第一通道渗流，其极限形状不是多边形，并且其极值点在边界中任意密集。因此，相关的理查森型生长模型可以支持可数无限数量的不同物种的共存，并且感染图具有无限多个端点。
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.