A STOCHASTIC ANALYSIS OF SUBCRITICAL EUCLIDEAN FERMIONIC FIELD THEORIES

• 成果类型: Article
• 署名作者: De Vecchi, Francesco C.; Fresta, Luca; Gubinelli, Massimiliano
• 署名单位: University of Pavia; University of Bonn; University of Bonn; University of Oxford
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1714
• 发表日期: 2025
• 页码: 906-966
• 关键词: feynman-kac formula; gross-neveu model; renormalization-group; Conditional expectations; expansions

摘要

Building on previous work on the stochastic analysis for Grassmann random variables, we introduce a forward-backward stochastic differential equation (FBSDE), which provides a stochastic quantisation of Grassmann measures. Our method is inspired by the so-called continuous renormalisation group, but avoids the technical difficulties encountered in the direct study of the flow equation for the effective potentials. As an application, we construct a family of weakly coupled subcritical Euclidean fermionic field theories and prove exponential decay of correlations.