GROWTH EXPONENT FOR LOOP-ERASED RANDOM WALK IN THREE DIMENSIONS

• 成果类型: Article
• 署名作者: Shiraishi, Daisuke
• 署名单位: Kyoto University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1165
• 发表日期: 2018
• 页码: 687-774
• 关键词: uniform spanning-trees; limit

摘要

Let M-n be the number of steps of the loop- erasure of a simple random walk on Z(3) run until its first exit from a ball of radius n. In the paper, we will show the existence of the growth exponent, that is, we show that there exists beta > 0 such that (n ->infinity)lim log E (M-n)/log n = beta.