Critical exponents for a percolation model on transient graphs

• 成果类型: Article
• 署名作者: Drewitz, Alexander; Prevost, Alexis; Rodriguez, Pierre-Francois
• 署名单位: University of Cologne; University of Geneva; Imperial College London
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01168-z
• 发表日期: 2023
• 页码: 229-299
• 关键词: gaussian free-field; renormalization-group; inequalities; clusters; systems; set

摘要

We consider the bond percolation problem on a transient weighted graph induced by the excursion sets of the Gaussian free field on the corresponding cable system. Owing to the continuity of this setup and the strong Markov property of the field on the one hand, and the links with potential theory for the associated diffusion on the other, we rigorously determine the behavior of various key quantities related to the (near-)critical regime for this model. In particular, our results apply in case the base graph is the three-dimensional cubic lattice. They unveil the values of the associated critical exponents, which are explicit but not mean-field and consistent with predictions from scaling theory below the upper-critical dimension.