An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions d > 6

• 成果类型: Article; Early Access
• 署名作者: Duminil-Copin, Hugo; Panis, Romain
• 署名单位: Universite Paris Saclay; University of Geneva; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-025-01416-2
• 发表日期: 2025
• 关键词: self-avoiding walk; critical 2-point functions; critical exponents; PHASE-TRANSITION; lace expansion; lattice trees; models; inequalities; sharpness; decay

摘要

This article proposes a new way of deriving mean-field exponents for sufficiently spread-out Bernoulli percolation in dimensions d > 6. We obtain up-to-constant estimates for the full-space and half-space two-point functions in the critical and near-critical regimes. In a companion paper, we apply a similar analysis to the study of the weakly self-avoiding walk model in dimensions d > 4 [Duminil-Copin and Panis, arXiv:2410.03649, (2024)].