Tightness for the cover time of the two dimensional sphere

• 成果类型: Article
• 署名作者: Belius, David; Rosen, Jay; Zeitouni, Ofer
• 署名单位: University of Basel; City University of New York (CUNY) System; College of Staten Island (CUNY); Weizmann Institute of Science; New York University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-019-00940-2
• 发表日期: 2020
• 页码: 1357-1437
• 关键词: brownian-motion; random-walks; CONVERGENCE; maximum

摘要

Let CE,S2 denote the cover time of the two dimensional sphere by a Wiener sausage of radius E. We prove that CE,S2AS2 pi logE-1-loglogE-1is tight, where AS2=4 pi denotes the Riemannian area of S2.