THE TWO-TYPE RICHARDSON MODEL IN THE HALF-PLANE

• 成果类型: Article
• 署名作者: Ahlberg, Daniel; Deijfen, Maria; Hoffman, Christopher
• 署名单位: Stockholm University; University of Washington; University of Washington Seattle
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1557
• 发表日期: 2020
• 页码: 2261-2273
• 关键词: mutual unbounded growth; 1st passage percolation; 1st-passage percolation; ergodic-theory; geodesics; coexistence; absence

摘要

The two-type Richardson model describes the growth of two competing infection types on the two or higher dimensional integer lattice. For types that spread with the same intensity, it is known that there is a positive probability for infinite coexistence, while for types with different intensities, it is conjectured that infinite coexistence is not possible. In this paper we study the two-type Richardson model in the upper half-plane Z x Z(+), and prove that coexistence of two types starting on the horizontal axis has positive probability if and only if the types have the same intensity.