An alternative approach for the mean-field behaviour of weakly self-avoiding walks in dimensions d > 4

• 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
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-025-01415-3
• 发表日期: 2025
• 关键词: lace expansion; lattice trees; percolation; decay

摘要

This article proposes a new way of deriving mean-field exponents for the weakly self-avoiding walk model in dimensions d > 4. Among other results, we obtain up-to-constant estimates for the full-space and half-space two-point functions in the critical and near-critical regimes. A companion paper proposes a similar analysis for spread-out Bernoulli percolation in dimensions d > 6 [10].