EXAMPLES OF NONPOLYGONAL LIMIT SHAPES IN IID FIRST-PASSAGE PERCOLATION AND INFINITE COEXISTENCE IN SPATIAL GROWTH MODELS

• 成果类型: Article
• 署名作者: Damron, Michael; Hochman, Michael
• 署名单位: Princeton University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/12-AAP864
• 发表日期: 2013
• 页码: 1074-1085
• 关键词: 1st passage percolation; time constant; THEOREMS

摘要

We construct an edge-weight distribution for i.i.d. first-passage percolation on 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.