GREEDY WALK ON THE REAL LINE

• 成果类型: Article
• 署名作者: Foss, Sergey; Rolla, Leonardo T.; Sidoravicius, Vladas
• 署名单位: Heriot Watt University; University of Buenos Aires
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/13-AOP898
• 发表日期: 2015
• 页码: 1399-1418
• 关键词: spatially distributed arrivals; perturbed brownian motions; uniform spanning-trees; erased random-walks; SELF-AVOIDING WALK; conformal-invariance; SCALING LIMITS; systems; queues; plane

摘要

We consider a self-interacting process described in terms of a single-server system with service stations at each point of the real line. The customer arrivals are given by a Poisson point processes on the space time half plane. The server adopts a greedy routing mechanism, traveling toward the nearest customer, and ignoring new arrivals while in transit. We study the trajectories of the server and show that its asymptotic position diverges logarithmically in time.