Hitting probability of a distant point for the voter model started with a single 1

• 成果类型: Article
• 署名作者: Merle, Mathieu
• 署名单位: University of British Columbia
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117907000000286
• 发表日期: 2008
• 页码: 807-861
• 关键词: super-brownian motion; hausdorff measure; systems; support; zd

摘要

The goal of this work is to find the asymptotics of the hitting probability of a distant point for the voter model on the integer lattice started from a single 1 at the origin. In dimensions d = 2 or 3, we obtain the precise asymptotic behavior of this probability. We use the scaling limit of the voter model started from a single 1 at the origin in terms of super-Brownian motion under its excursion measure. This invariance principle was stated by Bramson, Cox and Le Gall, as a consequence of a theorem of Cox, Durrett and Perkins. Less precise estimates are derived in dimension d >= 4.