The fluctuation result for the multiple point range of two dimensional recurrent random wales

• 成果类型: Article
• 署名作者: Hamana, Y
• 署名单位: Kyushu University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1997
• 页码: 598-639
• 关键词: random-walks

摘要

We study the fluctuation problem for the multiple point range of random walks in the two dimensional integer lattice with mean 0 and finite variance. The p-multiple point range means the number of distinct sites with multiplicity p of random walk paths before time n. The suitably normalized multiple point range is proved to converge to a constant, which is independent of the multiplicity, multiple of the renormalized self-intersection local time of a planar Brownian motion.