Stochastic quantization associated with the exp(Φ)2-quantum field model driven by space-time white noise on the torus in the full L1-regime

• 成果类型: Article
• 署名作者: Hoshino, Masato; Kawabi, Hiroshi; Kusuoka, Seiichiro
• 署名单位: University of Osaka; Keio University; Kyoto University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01126-z
• 发表日期: 2023
• 页码: 391-447
• 关键词: GAUSSIAN MULTIPLICATIVE CHAOS; sine-gordon equation; dimensions; uniqueness

摘要

The present paper is a continuation of our previous work (Hoshino et al., J Evol Equ 21:339-375,2021) on the stochastic quantization of the exp(Phi)(2)-quantum field model on the two-dimensional torus. Making use of key properties of Gaussian multiplicative chaos and refining the method for singular SPDEs introduced in the previous work, we construct a unique time-global solution to the corresponding parabolic stochastic quantization equation in the full L-1 -regime vertical bar alpha vertical bar < root 8 pi of the charge parameter alpha. We also identify the solution with an infinite-dimensional diffusion process constructed by the Dirichlet form approach.