PARKING ON TRANSITIVE UNIMODULAR GRAPHS

• 成果类型: Article
• 署名作者: Damron, Michael; Gravner, Janko; Junge, Matthew; Lyu, Hanbaek; Sivakoff, David
• 署名单位: University System of Georgia; Georgia Institute of Technology; University of California System; University of California Davis; Duke University; University of California System; University of California Los Angeles; University System of Ohio; Ohio State University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/18-AAP1443
• 发表日期: 2019
• 页码: 2089-2113
• 关键词: annihilating random-walks; spatial structure; recurrence

摘要

Place a car independently with probability p at each site of a graph. Each initially vacant site is a parking spot that can fit one car. Cars simultaneously perform independent random walks. When a car encounters an available parking spot it parks there. Other cars can still drive over the site, but cannot park there. For a large class of transitive and unimodular graphs, we show that the root is almost surely visited infinitely many times when p >= 1/2, and only finitely many times otherwise.