Critical one-arm probability for the metric Gaussian free field in low dimensions

• 成果类型: Article; Early Access
• 署名作者: Drewitz, Alexander; Prevost, Alexis; Rodriguez, Pierre-Francois
• 署名单位: University of Cologne; University of Bonn; Imperial College London; University of Cambridge
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-025-01392-7
• 发表日期: 2025
• 关键词: percolation; interlacements

摘要

We investigate the bond percolation model on transient weighted graphs G induced by the excursion sets of the Gaussian free field on the corresponding metric graph. Under the sole assumption that its sign clusters do not percolate, we derive an extension of Lupu's formula for the two-point function at criticality. We then focus on the low-dimensional case 0 < nu < (alpha)/(2) , where alpha governs the polynomial volume growth of G and nu the decay rate of the Green's function on G. In particular, this includes the benchmark case G= Z(3), 3 , for which alpha=3 and nu=alpha - 2=1. We prove under these assumptions that the critical one-arm probability decays with distance R like R--(nu)(2) to multiplicative constants. , up