LATTICE APPROXIMATION TO THE DYNAMICAL Φ34 MODEL

• 成果类型: Article
• 署名作者: Zhu, Rongchan; Zhu, Xiangchan
• 署名单位: Beijing Institute of Technology; Beijing Jiaotong University; University of Bielefeld
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1188
• 发表日期: 2018
• 页码: 397-455
• 关键词: differential-equations driven; quantum field-theory; stochastic quantization; CONVERGENCE; burgers

摘要

We study the lattice approximations to the dynamical Phi(4)(3) model by paracontrolled distributions proposed in [Forum Math. Pi 3 (2015) e6]. We prove that the solutions to the lattice systems converge to the solution to the dynamical Phi(4)(3) model in probability, locally uniformly in time. Since the dynamical Phi(4)(3) model is not well defined in the classical sense and renormalisation has to be performed in order to define the nonlinear term, a corresponding suitable drift term is added in the stochastic equations for the lattice systems.