The subleading order of two dimensional cover times

• 成果类型: Article
• 署名作者: Belius, David; Kistler, Nicola
• 署名单位: New York University; Goethe University Frankfurt
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0689-6
• 发表日期: 2017
• 页码: 461-552
• 关键词: brownian-motion; 2 dimensions; random-walks; asymptotics; trees

摘要

The -cover time of the two dimensional torus by Brownian motion is the time it takes for the process to come within distance from any point. Its leading order in the small -regime has been established by Dembo et al. (Ann Math 160:433-464, 2004). In this work, the second order correction is identified. The approach relies on a multi-scale refinement of the second moment method, and draws on ideas from the study of the extremes of branching Brownian motion.