Shape of territories in some competing growth models

• 成果类型: Article
• 署名作者: Gouere, Jean-Baptiste
• 署名单位: Universite de Orleans
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051607000000113
• 发表日期: 2007
• 页码: 1273-1305
• 关键词: 1st passage percolation; spatial growth; coexistence

摘要

We study two competing growth models. Each of these models describes the spread of a finite number of infections on a graph. Each infection evolves like an (oriented or unoriented) first passage percolation process except that once a vertex is infected by type i infection, it remains of type i forever. We give results about the shape of the area ultimately infected by the different infections.