One-arm exponent of critical level-set for metric graph Gaussian free field in high dimensions

• 成果类型: Article
• 署名作者: Cai, Zhenhao; Ding, Jian
• 署名单位: Peking University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01295-z
• 发表日期: 2025
• 页码: 1035-1120
• 关键词: critical-behavior; local-times; percolation; clusters; inequalities; asymptotics

摘要

In this paper, we study the critical level-set of Gaussian free field (GFF) on the metric graph Z(d), d > 6. We prove that the one-arm probability (i.e. the probability of the event that the origin is connected to the boundary of the box B(N)) is proportional to N-2, where B(N) is centered at the origin and has side length 2 left perpendicular N right perpendicular. Our proof is highly inspired by Kozma and Nachmias (J Am Math Soc 24(2):375-409, 2011) which proves the analogous result for the critical bond percolation for d >= 11, and by Werner (in: Seminaire de Probabilites XLVIII, Springer, Berlin, 2016) which conjectures the similarity between the GFF level-set and the bond percolation in general and proves this connection for various geometric aspects.