Formation of an interface by competitive erosion

• 成果类型: Article
• 署名作者: Ganguly, Shirshendu; Levine, Lionel; Peres, Yuval; Propp, James
• 署名单位: University of Washington; University of Washington Seattle; Cornell University; Microsoft; University of Massachusetts System; University of Massachusetts Lowell
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0715-3
• 发表日期: 2017
• 页码: 455-509
• 关键词: internal dla; fluctuations; aggregation; models

摘要

We introduce a graph-theoretic model of interface dynamics called competitive erosion. Each vertex of the graph is occupied by a particle that can be either red or blue. New red and blue particles alternately get emitted from their respective bases and perform random walk. On encountering a particle of the opposite color they kill it and occupy its position. We prove that on the cylinder graph (the product of a path and a cycle) an interface spontaneously forms between red and blue and is maintained in a predictable position with high probability.